00020001010008main.ACT0009020017SolveProblem_WeiChi.EAC010000000915É SolveProblem_WeiChi.EAC† main.ACT†'†* ˆ7†;† Žˆ†N _E †(Œ'[ˆg†[-†\'s pŒm:ŽR†‡Ž&define g(x)=-x^2-1RŠiˆ«done–.sˆ¼(†' +(y-1)^2=1,y)Š2†«ˆày=-Ž -xŒ2Œ˜+1Ž)+†==¼,’5еŽc޶fˆ¶1-Œò1ˆÁ¶¿ diff(ˆë,xŒµŒz-2î’x–)‘2† doneR† †&solve(((g(c)-f(x))/(c-†*gˆ+1=0,c)RŒ52î’cŒA3Ž -x-cî’Ž%†%Ž-x12Œz+15ŒŒ=0–š\Œ¢Sˆ¢ for c, given xåˆ$†(åŠ.üN SpreadsheetSІˆÈ+B†ä† (@PŠ † (@ˆ7 x†  †ˆ† †H8!ˆHˆLˆˆ# ™¨'†.È'ÌNˆ ÆuÌœÌÃÌê Í Í8 ­_žD†cˆ†±††J†† ' Ì'ÌNÌu†N†N†N†N†NÍ_µ†–’šN Nˆ¹˜'†RÌN†R†R†R†R†R†R †R!žR"ºR#†R$ÌN%†R&†ò '¨Ã(†Æ‰}(&solve(((g(c)-f(x))/(c-†*gˆ +1=0,c)t`†ôììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†ŒŠ Š,–7––ª`†ºþqŠq†>ŽþqàâþâãSËSq`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†ŒŠ Š,–7––ªþq˜qþqââþâãS ÅSqª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!† ’gŽFœE†d°S–B†ŒŠ Š,–7––þqžq þqââ þâãS ¿Sq–ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†ŒŠ Š,–7–þq¤qþqââþâãS¹Sq––ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†ŒŠ Š,–7þqªqþqââþâãS³Sq7––ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†ŒŠ Š,–þq°qþqââþâãS­SqŠ,–7––ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†ŒŠ þq¶qþqââþâãS§SqŠ Š,–7––ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†’gŽFœE†d°S–B†Œþq¼qþqââ þâãS!¡SqŒŠ Š,–7––ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†"’gŽFœE†d°S–B†þqÂq#þqââ$þâãS%›SqB†ŒŠ Š,–7––ª`†ºììtBF z Š ÿg†cކ"€ˆ Œ)fš)!†&’gŽFœE†d°S–þqÈq'þqââ(Èâ@‰E[9eActfH x1-à(1-x^2)gH x-x^2-1ggHx-2*x020010distance06-2.EAC01000000593fÉ distance06-2.EAC† main.ACT† †# ˆ0†4ІG^I ˆŒ'%[†3ˆd Example 1ˆs Œ'-Consider C1: x^2+(y-1)^2=1 and C2: y=-†-1. †M†°5For every point on†? , we can fi†9the correspondingŽq?”22 so†(atŠ-‘ isŠ= shortest from†ž to C2.\Œ¸"įΉ‰'ÎC‘,‹H dI)Wƒ† `P„PpBWŠ ŒX‰› ˆ A‰§˜Dv‡¹†r† Ž A† † †L† †&Œ C˜ u˜x˜yŽ †_† †9ËÀ! ŠK6@†Ð6–°†%V3€(&†&`a† e† ŽCŽJ î : ÿÿü†ž†- ŽpÈÈ Œg–f ƒ1H„E†ð Y™‚V„1c† ™qV ‘І3ŠBÀ ¤B"R 3•`ŠB t’yˆ‡ Y™Prx‡JY˜‘Ž˜‰R9†NŽ÷5š÷`”÷—0‰P¢÷ Length DA¬þ†† ÄÈ  †A@†Ð6–°†#W(W(†. Y™ ƒb$H—–Š †7†:ІJœCD˜C"R 3•`ŠCPrx†} ˜žC†‘ †–9ÈÀ ŒG4˜ŠdV3€(&†&`†¤Gˆs#q† ˆKšŒSlope of tangent at A: ÿÿü†žr† †zÈÈ"‹—‚V„1c†À ‡1H„EŠ "“†@$˜… ŽÀŒÀ3œÀ”Àƒ—0uÒÀD¤À††Ž †9ÈÀ  ˆ!2@†(Ð6–°†/cV3€(&†& `!vc7y† Ž:ŽA Coord of A: ÿÿü†ž%ŒŠ †9Ë’w1²wADƒ¼wDÂwއ1Ä@ŽîˆŠ•DHŒ‰E™P…R8‡: ˜™u‹ ˜ÊÀ!”U-(íëx+0.45)^2-0.975†H†‡ˆÅ ‚‰Žˆ‡¦5Æ@!’ˆº‡¤È ˆ  @†Ð6–°† ŠŠ’ – 8wU S†< ™”1Y™P ™S$H˜†` ˆ†iÄ@  Gˆ9††šŽŠH–†¯ÀH"ŠFB–¹“7ˆBŠ•˜$yhй˜ÑŽs†öŘsˆYˆ;ˆ†w5š‘‡&ˆô@‚Šé°õsF“‡uQõ†J!šJ †ª W–2g”‰f‹{¢ˆqˆˆ“‡£.ɘ‡µ3ÈÀ  ††† ††.É@ š††/.ÈH!”ˆ4ˆŽ<ˆ"ˆ@ˆˆˆa1ŘLˆ2ˆPH†–z†ˆ!Žˆ“†–%† † † † †Ž<ˆÓ2ˆ † áRˆëˆñdefine g(x)=-x^2-1RŽdone–.solve(†' +(y-1)^2=1,y)–2 No SolutionŠgŒJŽhfˆh1-Œ~1ˆs¶q diff(ˆ,x˜g-2î’x–È!define g1(x)=-2xRdoneRˆ Œ&solve(((g(c)-f†1 )/(c-x))*†? c)+1=0,c)ŠBŽE2î’cŒQ3Ž -x-cî’Ž%†%Ž-x12ŒŠ+15Œœ=0–š ŽÆhŠÆ¶Ã¶ß†’ë\Ј!† ÊŒ N&L%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡Ìxy†^‰Ø<†U†y2‡ †³8†i†ä†€L´ä<‰TŠÈäŽP †W †ä† † ‡np’Š©†Ý’†Þ;’”’’ ’’¬’’¸’’Ä’’Ð’’Ü’’è’†ô†ðŠùŒ ‘ †!‘ˆ¾†"‘,$†#‘@0’ˆ‹W<†%‘hH† &‘|T† '‘`† !(‘¤l¸†ä)†x†  †*†y„†}+††,†œ†-†¨†.†´††pÀ†1†̆2†؆3†ä†4†ð†5†ü†ÉEð†F†Ê† H‘ † I‘,ˆú†ÓJ†Ê8†K‘TD† L†ÊP† M†Ê\† N†Êh† O†Ê t’ˆF†Ë€††Æ†Ú Q††Œ†R†ƒ˜†S†¤†‰°†]‡h ¼†i ˆ^ŽÐ_†Ć‰,ȆaŽàb†І”†Ô’Œ•†à† ͆ì†Άø’ˆZ‹ ’ב,† Ø‘@† Ù‘T(† Ú‘h4† )Û‘|@‘ Financial‡ª Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡X‰c ††† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è†]–|œš"˜| “i™” ™‰G‰K† &“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´ˆ²††°† Š” †#’$†(œ†AŠ +†V! 3x(-(-4*x+4*(-x^2+1)^(1/2)-7Ž )/†/2’O(Œ<Š<º:Ž9†›Ž;`– PÎÆ$´$“– –0” – •%i™`‡e —‰@`Y†Û# ™˜<™€(1…0qy`‰X#Y‡uYƒ‡­ ˜–‰»‰ ‡ƒ;Ž ˆ – ˜Æ$ÊH’ ’¤È%°´þaþ þߞجð`@» —’e5‰y`” – œ†ˆ$†Xˆ \ŠΈ"† Έ† Š/Š™™™™™™†`V%Œ6† Œ˜† –˜DvŒd†K†r†  A† ŽkLŒ‹ŠxC˜ u˜x˜yŒ¿†qˆq#†äˆ@  Œ -íëx^2+-1†ˆûˆ!Œ@‡Ð6–°† Š÷4ŒÖ– ׉BˆjˆˆŒâ[O[Z)(step1: construct two curves, C1 and C2. Ž0 step3: fix the curve C1. -ˆ 2: construct a tangent to† Œ1 at C2. Œ6LŽV˜6perpendicular lineˆAˆtPІJ a given point‰NˆS4: sele††ˆ¬inters† ion betweenŠÅnormalŒdand†Ï (**sometimes we Ž©can†/t‡nd‡ is using CP)zQˆz 5: animateŠbŠ› (which†O•eˆFœÓ) along‘[‹'(J&step6: collect point C Ion C1) and theŽA ˆ2 afterŠanimation. .ˆQ7”QonlyŠB x-values for†aˆYA. Œ6Ž>7T†lfirstˆ’umn=x Š7Šy1 (wˆ †R concentratˆ ŽH/”¬that isˆ²low†¯half ofŠÏcircle´&ˆvseco†íŽw –x‰C2–¬2Œð -0.7526798709Œ†25´ ˆ4 2397959184´Hˆ\22Š&367®p -0.2193877551†Š 8324367047”20918†35”( 745403719–1989795†-”P 680830956–<18Œv02”x6256758†}”Œ 1785714286” 576195262–´16Šž469”È53064†64”Ü 158163265–d 488014869–d14ŒÆ3— 447671078Ž †d13¢Ç4‡+62†;—S12Œí0–‹ 372157965˜Ÿ1ŠÄ38—?33640429“?-0.1071428571 † 3016986366Œ†( 0969387755–) 2678748608–)86734ˆ-Ž †f 234792892–( 7653061224”z 2023324919–)6632Œ,”£170†Ž6503–)5ŠN489ŽzˆÌ138†Ê818Ž=ŠÌ 4591836735”{‡ 674392˜{3‡™޹7393579˜|2‡0204‘ ‰Hˆh82957ŽâŠ)1öŽ|325995ŽS-5‡šŠO16îìëŽç ŠA28260†W5.102040817îìë3ˆ 0.04593284732” 1530612245Œ †( 766890038”'255ŽV’'1†(236359”' 357142857Žb†N1388125†bš‰183673”u 1703357756”°5Š™489Žu 0.20227979–M66326ŠÆ’t23†å9217–M7Œ$22”é 2678199907”'8†–46938”é3016423†”'9ˆ#†®5”u3‡ 46385r#”› 372098048”®11’s 0.4090998654 127551020” 4476058565Œ 0.137Œ'’8 4879460267”K47959183” 5305682809”q 581632653’„5761†971”&68367346”962558†J—†9 1785714286’˜6807†u7–_188 ¾745†•16–ö19†ŠÀ’¾ 832236188”˜20ˆá673”…¨&193ŒtºL2/—C¢r0.2397959184 0.8322361881Œ†&5\Œåˆ%† åŒ LN SpreadsheetSІˆÈ †ä†† 2@ˆ † 2@†Rg˜p†DY™¯á´´Ò62Cgp¬lE@7Pª‡€ƒ V®%gX$0ª½vRbªØ0d†‡¦óˆHi`«Ggx¬½ !ƒ¬lrye”l@6@B–PY™¯áši†6`ªg‡H`€ª64y(’ˆP¤Q3$‘ªlp8vP0ª‡8†8ª¢gC’¬Qg95yŒQ˜žØY‚•tŒ¢ S2Y•¬6R‚`•pˆ ¤Q2„s ªf‰8‰^¤6b65н ¡z8%"@¬p3Wu` ™¯á@'—”ˆ¦4s’®6g™pªQd#†®64c…0ª‡r €Hª¢ ˜e@ª½G`XVPªØ‡”`&¬¢0V‚€«vX—¬‡%X€–¬l€su¬ØE(`¬½2#aˆ¬ó¬2#aˆ ™¯á@´¬2˜9PˆPˆY T9yY@¬)Y6p¬68wUŠo¤Q 6sŠp¢l˜—•‘€ª‡ˆ†P ª¢xW(`ª½h6sFªØX2e0ªóG•‘ƒ¬Ø7uQ‡„©)'U ­)4i8ˆØY™¯á@(W¤ i8wUŒ˜ž6g4i8€ªe0a"@ª6c&S¬Qa"D‰¬QY6sPª‡W’½ ¢U @¬¢S$¬Q†5`Š—¨pˆ  ”Q ¡)”‡¢н ª6”ó Q"a"D‰€ ˜¯á@c&Sªe0a"Pª6g4i8¬Q i8wU¬Q(WŒ™ž‡’Q¢'U @¬67uQ†ÄªQG•‘ƒp¬lX2e0¬‡h6sF¬¢xW(`¬½ˆ†ò ¬Ø˜—•‘¬Ø 6s_¡“D‹)@)Y6p ™¯á˜9yY@¬Pˆ2”62ކXˆR!7c† `7 ˆ %>Y™”  ™†“kˆ'a” –Š—[ˆ¹\Œ(6Look at when x near 0.5, we get c about†10 somethingÔˆF&ÊŠˆ£DN&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°h† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡–  ˜9“˜†Ì Y™ ˜p4w8†Ø ™–„”x@…$†ñ —’Y†ª4œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH2#aˆ‡ * ™PˆŒ ž¢;– àHàxਚ2Œ¸†¼‡†ë$s<†H†T†`†l†x†„††œ†¨†´†À‡«̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆa@† LRg˜pY™– – œ2CgpŽ0E@7PŒ<€ƒ V %gX$0ŒTvRbŒ`0d†@ŒlˆHi`ŒxGgxŽT !ƒ†Crye†K86@B–Žli†6Ž<g‡H`€ŒÀ4y(’ˆË†Ì3$‘ŽØp8vPŽ8†8ˆXgC’üg95yŒ´˜Y‚•tŒH˜S2Y•Œ<˜R‚`•Šü †$2„s Œ f‰8‰C†b65ŠT ™8%"ŠÀ† p3WuŠ´†'—”Œ0™4s’g™‹†-"d#† 64c…ŠÀ ‡ €H‰P ™ ˜e@‡4ˆ YG`XVPŽ ‡”`&pŒ0V‚€Œ$vX—Œ0%X€–Ž0€su0ŒHE(`ŽT2#aˆŽ0– ®œ2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†oø(4@L‹XˆØY™9yY‹ † )Y6‹h†8wUŠü†$ 6s‹\Y™˜—•‘€Œ<ˆ†# ŒHxW(`Y™h6sF‡a'X2e0ŽG•‘ƒpŽ$7uQˆ/ˆ0'U @Ž<4i8€Ž‡_ (WŒT i†l!Œ ˜g’$˜e0a"Œ<˜c&SŒ0˜a"D‰DŒH˜Y6sPŠœ˜†§ŽT˜ˆwŒl˜S$Ž$†ŽŒÌ—Š Š´ —”$ –< ŒT Œ”l†„†œ Œ´ŽH”Ì ˜”äˆ8ü —† “,†“D†$“\†0“t†<“Œ†Hx‘¤†Tˆ†kŒ´™˜—•‘€ ™ ˆ† ˆ 8wUŽ )†¢#pŽ9yY@Ž$Š,Œ0 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†Uø(4@LRg˜p‡#Y™– – œ2Cg‹0†0E@7‹TY™€ƒ V %gX$0ŒTvRb‹lY™0d†‹`Y™ˆHi`ŒxGgxŽT !ƒŽ0rye‡ Y™6@B–PŠ i†6`Œ g‡H`€Œ4y(’ˆ#†03$‘Œ0p8vP0Œ<8†8ŒHgC’Ž$[g95yŒ$˜Y‚•tŒH˜S2Y•Œ<˜R‚`•pˆ  †$2„s Œ f‰8ˆ›†b65ŠT ™8%"@Ž p3WuŠ´ ™'—”†w™4s’g™Œ`™d#† 64c…ŠÀ†*r €HŠ  ˜eŽ`†ö`XV‹ †F‡”`&Œ¨‡V‚€ŽvX—Ž<%X€P†h€su†43E(`Ž´2#aˆŽl– ®œ2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†ð†wü ,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LP† Y™9yY@Ž )Y6pŽ8wUŽ$ 6sŠ4Y™˜—•‘€Œ<ˆ†# ŒHxW(`ŒTh6sFŒ`X2e0ŒlG•‘ƒŽ`7uQŽ„'U ˆB4i8`(WŽ„ i’˜g’$˜e0a"ŒÀ˜c&SŒ´˜a"D‰Œ¨˜Y’À˜†§W ˆ´Y˜U @€Œ S$PŒ†`Š —†pˆ  —”$ –< ˜†© W ŒY6sŽ$Š[Ž$ŠlŒ<Š~ŽHg†¡† i‡Ž$†TŒ ™’$†'ˆyŽˆÕˆËˆ$ˆæŒ¨™ŒøŽ<‹ ŽH"x†©ŠØ†Tˆ†kŒ´™˜—•‘Ž` ’À™’†J)†Ù™9yYŽ„‹4Œ¨ ˆŠõ¦`‹d\’e5‰yˆ” – š†ˆ Xˆˆ[Š Remark: Show this anlytically. Ž' ˆK Example 2.\ŒA (x+2)^2+(y-ˆ=4Έu'†gΈn† ŠˆŠp(Xh†† `s‘hƒ@†`%ˆ‡†Sˆ0†йDvŽÂˆr† Ž A† ŽkLŽ'‰C˜ u˜x˜yŽ ‡-ˆq(‡=5ÄH! ‘7)‡OÆÈ  D@†Ð6–°† “‡uQ† ™uˆPG†$`†(†ŠŠ*†9ÈÀ   -íëx^2+-2ŒCŠCˆIŒ<Y™˜D2f† ˜†+†ˆ2À@–O,†š@HŠaEš¤PUA†¼Y–I†Ç ¤-†ÝAHŽCF˜ç •&E‰D†ÿ Y•˜P9¨C.‡ Ř˜ˆU/‡6ˈ# Š—?’;`” – Šd0ªX1‡U•U–° 26‘tp#‹HaPuhGH‹£ 6‘q ™†-† 2† Å@  † †,†/†3†'Ä 1–"4†I!ÇH–"5†[ÈÀ@†jÐ6–°†qaPuhGHŠ| 26‘tp#Šˆ‚––QC†.†˜ 1W–2g”‰fŠ@6¢¡)އˆ‹7†q.Ș8†3”ƒ†*Ž4ˆ9¢0ˆˆ4:¢Jˆ4ˆˆdˆ<ˆ"ˆ@ˆˆ;‡!1Ä@!œ2ˆPˆæ<‡fÊÀ– -íëx^2+-‰t•Ž ˆ0¦ˆÚ‰a‰i‰¥‡±2(††† [2† -3.044445151Œ-0.5 2.887509543Œ † 4897959184”'76420461ŽŠ'Œ%367”N6585292šN6938775€ˆN5†N1653Ž:Š'ŽL3–œ47801798˜œ’”Ã3†¯82899–'Žs02”ê 322826416–'28571428ŽˆÃ25164573˜'Šæ346Žb‰8183†b61˜u08163265ް‰_11870707—8ˆ¯‰^þ -2.056039352 -0.38775510’ 1.995448424Œ ˆ&Ž%0ŽŠ'3666736Ž:Š'†469388”N 879471899–'571428†”u8236707›ŠuŠKˆŸ”œ 769098183–'vŽbˆÃ71†ê9076–'26530612–ê66307†ìŽaŠ'16Ž*”N61137841’¯†'ŠJ44–t‡\415šÂ295918‰Œ †M‡l090‘I‰]‹ ‹”M4‡©1179Žû -0.2755102041 -1.41099718Ž ˆ' 653061224”' 362067023–'ŽM08”N 313445597–N 448979592”N†b05986ŽaŠ' 346938775”N216838†+–'’O”N†&71153˜N14285714ްˆê1206093aŠ'ˆ¾1632ް‰0724616”¯0.1Œ™5$ †M0241976ކ‰618367ˆÅ–Õ97574443š(Š%†ê7ˆÖ92‡[6‡<—_ˆ—‰­ -0.8779634832 † 1530612245” 8284726494–(42857†9”< 778463228–<1326ŒS”P72783725šx†s489†‘”P 6764867528Œ †´1Ž)Žˆ; 624291512–³ 1020408163”O†¯11451Ÿ‡ 0918367346–È 516798247˜)ˆLŒË•-46115†¦37–)‰‹–{ 403965459˜)‹gŠô•W34‡f4698ŽŠ)5’Ψ-0.2837326024†040816†53Œ ˆ) 198329558” 0306122449”( 152505707˜Q2’S– 804638348ŽfŠ1’,Œ-9.950126459îìë5Œ¨0\Œ± scatter plotÔˆÅ=†ÉʈÏ|N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– 4ˆyqYtŒx3Pcp‰†Ù ™–„!—’G †ñ —’éY–$œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH •&E‡ %Y•ˆˆ Žœ¸†’ – øTøÊÌ2Œ¸†¼‡v†â$j<†H†T†`†l†x†„††œ†¨†´†À†̆؇ªä †ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆx@†LDE`ˆu T0Ž vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A`ŽT%Es 7ua$‡``95 Œ„™THBŽx“fg6‡”q†L‚6pu0v˜Ž´qV Žxf0tHPŒØaxAŽäV’<Qˆû†üFy0A —6 gˆ14EYކ)&PY† !h8Pl‡S8 7„$aiäA—i†’ utD6‹8Y™ 'a4‹€† w–4ƒ‹†(G&I‹Œ†xF2(ˆØ Y™'ƒrS ‡- † vHgR€‡-$)PŒAqE y‚GŽagcpŒ<–TYŽ D”F˜ŒTƒs&@Œ`ƒ)UŽ`RPW†3"cƒH0Š„˜ •&EŒ<•2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†aø(4@L‰c‰g‡t‰yY† 6‘Di8wUŒY6s€H—•‘˜ˆ#°(W(`Y™†"FŽ 2e0Œ†+ƒpŒ$‡uQˆ/†0†N @Œ<g4i8€ŒH†SW‡yF“‡uPŒ`†_“Ž`&S ŒxˆkŽ„$IŽ`†wg†…qB…Ž„† ƒŽ`e0a"ˆˆ†.D‰yYŠ.›w†>"$H—•Žä(WŽäˆñŽä†³QŽäƒ†Ùˆs†Íˆc†ÁŠË$ˆ B†©D‡Baˆ "†‘h$H˜ˆ4ˆyh •€˜‹˜˜”¨˜†Á¤˜‡~` Y˜2e0† † ŒÍ)†ˆˆ`Œˆ Ž$ŠŠ$’ ” 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†$ø(4@LDE‡ #`ˆu T‹$† -vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A‹T†:.%Es 7ua$‡``95 Œ„™THBŽx“fg6† †lT‡”q‰Š ‚6pu Ž v˜0ŽqV `Ž$f0tHPŽ0axAŽ<V’<QˆSˆ`Fy0A —06 g†s014EYpŽ„&PY†@Ž!h8Pl‡S 7„$ai´A—i†– utD6ŠØY™ 'a4ŠÌ† w–4ƒŠä†(G&IŠl†xF2(Š('ƒrSŽ$vHgR€ŒH$)†²qEŽ0y‚GŽ<agcŠÌY™–TŒˆd D”F˜Žƒs&‡Aƒ)UŽ`RPWŽcƒH‹€Y˜ •&E‹¤Y•2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†_ø(4@L† Y™‰yY@Ž † 6pŽi8wUŽ$Y6sPŽ0H—•‘€Ž<ˆ# ŽH(W(`ŽT†FŽ`2e0Œl†;ƒ†‡uQŽ„† j Ž„g4i8Ž`†SWˆF“‡uˆ6sF“†@&Sˆ0ˆkˆ.$IŽä•‘ƒgŽ„…qB…p ˆ®Y™†Z Ž e0a"@†ªU @€†ªD†Â †ª†jwPŽ<$†³†¬†­0†¬†¥pŒ`†{Qˆk†lƒ†—†¾s††Æc†‡Ž„AS$Ž`B…qBŽ`2†Ž„"†‘`ŒÀ$H˜`ˆyŽ„ 6sFŒœ˜†Že0Œ0˜”¨†djH—ŒÀ˜†ïŒT˜ˆ¿eŒÌ˜†IŒÀ˜ŠØŒx˜–lŒ‰O Ž ’ ‹a¦`ŠÈ‰Œ —’e5‰yˆ” – š†ˆ Xˆ†[Š Ž Example: Another eŒ Œ)\Œ1 animationΈ>†ÎˆVŽ\ŠwVYrq’† `9ef‰•Š ’G5‘'† @ˆ™Š ŽDˆ³v’K†r† Ž A† 'LŽ'ˆçC˜ u˜x˜yŽ ‡?†Æ@  † †@†ÁH"ƒŠGˆÐ6–°†-D‰X’BE†& 4u„g€†Š <Ž A†Y ÈÀU–B%‰‚ƒ†z ™ t'pˆp Y™•xaF23Š †3B†BÈÈ ƒ`Š…E˜…Ph¶†Ož…C†ÞÉÈ ŒCF˜È”7˜ùŒz˜CD‡!Ä™ˆ˜ˆÞ‰ÅH–ˆoˆ†lF‡YÇ¡UG†‘ÉÈ!¥@"p„‹ h!G !R‹"77#5ˆ¢‹dˆFHŽ”†F†I†ÈÈ ƒ`ˆC@†Ð6–°†€Ž%` Ž  ™’ ŒJ†C ÈÀ! Š–B)€XB†6 Y™vuWHq•Š 4V3Q1І3CމK†•Ä@ ŽJŽˆ`H†1Ž"ˆE†D†AŽ$LŠ:H–:B†MŠšÈ–Ü h€†0ŠÐ)#IX–ŠÜ&ifH49Šô†N"D™ˆ…ŠYP” Ÿˆ‰O¢ŸˆYˆŸL Ž"ˆˆ.ˆL¤.Q‡² ËÈ#gÐ6–°†R2—X€b† Y™ 5‡Y!‚‘† ™Gd‰T˜†*`†.I† N†R†;ÄH  † †ŒQ†QPÿÿÿÿŽ"ˆˆ.ˆS†m5Å@!’2T†DÄÈ ŠDA@”Šn†&6†¨ƒ?†½U†ÂÊÀ!”‡-(íëx+-1)^2+-4˜H«ˆ×PC yHqyHr‡  ˆèV‡Ç@–ÛW‡(ÃH©B¤©–©ˆ ¢©G†XŠYH–­ˆYY†ÃÊÈ‘—h!G !ˆª ™@"p„‹” V ”t…†W† Z† !Ä@  † †Y†GW–2g”‰f€†[†4Ř'T†G††\†R.È@ ’]†d3ÉÀ!”UŽ4ˆ_^†‚.ËH–0ˆˆ4_†œ.ʘˆ4ˆˆdˆ<ˆ"ˆ@ˆˆ`†š1¢šˆPH–vžƒˆ·‰I†N†Q†B†M†C†A†J†@(ˆAS‘$ [(‡L -0.5229403823Œ0.8” 3946122586Œ 0.8179487†”E 264952635Ž;ˆ'† 97435ˆ' -0.1338658196† 0.8538461†Œ-1.252210698îìë3”+71794†Ž+†> 1329899095”Q 897435897’d 268966744”& 907692307”&4067†ž94”9 925641025ް 0.546562241’Â9Œn43”Õ688409†˜4’„9Šäˆê”û 324496012’ã9Œá7–Ð978805‡•49âŽ_ 1.1276045- 1.0œo†2789807‘iˆ$3333†”643‡006ޏ 1.051282† 1.590014988’ 069230769’$74996129”6 087179487’H 913061434’Z1mŽ2.0†372246’~1Œj23’$24935616”14102564~ 2.42288213”´15897435´2.600†j522’ê1Ši07´ 2.78156478¢1.1ˆÔ†Ú”´96709031”´2CŽ´ 3.156‡!’é1.Ö³ 3.3514836–³2Œj4³3.55‡v341”26666†‘g3.755053048 1.284615385Ž 3.964578506’$ 302564103Ž 4.17957508”H 320512821’$4002871˜H3Žm’H62696877~1.3Šj†p’l85988425Z 1.374358974Ž 5.099308679’Ø 392307692’$34552861Ž$ 1.Œi4Y5.Œj33”k428ŒÙ’k85956060”³4B4³6.‡ 00†¥‘11.4ŽÖ޳ 6‡45209•f4Žj² 6.68945373œ 1.5[\ŽÔˆa† ÊŠ¨N&à%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H„ ˆ^<̇P_PP†iŠ`dˆZ†faxˆãbŒ\† d †FŽde´ä†”Èh’´•Üt†Íð€†ΑŒ† Б˜† ב ,¤’Ø‘@°† Ù‘T¼† Ú‘hȆ 8Û‘|Ô‘ Financial‡ªForma†¾ †††Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– W&DŠx8–Š$–„B˜9UW†ñ ˜pê ™”`˜0™ (1…0qy`ˆä#Y‡uYƒŠH–˜œšH®Æ$ÈH%"i€‡/Y—qyHqŠ  ™ˆˆŽœ¦’ – àHàxਚ(Œ¸†¼‡~†ê$r<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Oü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDtÔ"”‚0‹ ™”a"X`‹¬™d•&5‡¸ Y™3†X`Š %"i€Š —2˜™ Pˆ ™h–gDŽ xe”pŒFV"Aˆ;†$ˆ@™@Œ02D– Œ< x€QŠ`†7UvSˆk'‰€sŠl† C0pŠ<†Y˜t™a)Ž$‘0aCŽ$”r$Š´$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÌˆ$–p1Ž<i–Ž5ƒcˆ$UcAŽ0uPSލ–ExPŽx•uŽÀ@‡†0ObihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ( † ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ†£0 ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i#†}%d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( QŠx †P#†ˆо $‡”†¹&fffpŽ(F8PŽ$0†¥0Ž02†u<3ŠÑH5ˆ»ŽT7†»@Ž`9†m ŽlAVAˆwˆxB‚†DaS„&<F†%<H Q(<ŠŒŒ´ (†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ"”‚‹DY™”a"X‹,† d•&5Š3†XŽ%"i‹\Y—2˜™ ‹Œ ™h–gDP ™xe”pŒ FV"Aˆ†ˆ@™@Œ$2D– Œ0 x€Q`Œ<vSˆG '‰€s€Ž C0pŠ<†Y˜t™a),Ž$‘0aCŽ$”r$ŠT$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÀˆ$–p1Ž<i–Ž5ƒcˆUcAŽ0uPSލ–ExPŽxg•uŽÀ@‡ŽbihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ(† † ††$†0†<†H†T† `†$lx†)„††œ†¨†´†À†̆؆ä†ð†Nü ,8DP\ht€Œ˜¤°¼ÈÔ† ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i# %d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( Qx#†Ùx$‡”x&]fffx(F8 P0%d0Ž 2‚Ž3„aS€Ž$5d%`Ž07CX—@Ž<9#i ŽHAVAˆSˆTB‚<DaS„<F†%† 6H Q(<ŠŒŒ ˆ®`VŠi†Í ˜’e5‰yˆ” – œ˜`†‰XˆŽ†’[Œ eActfH x1-à(1-x^2)gH x-x^2-1g1Hx-2*xh1H@/x((-à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))h2H@.x((à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))020011distance06-2a.EAC010000005f48É distance06-2a.EAC† main.ACT†!†$ †.ˆ1†5† ІH^I ˆŒ'5[ˆ7 Example 1ˆt Œ'-Consider C1: x^2+(y-1)^2=1 and C2: y=-†-1. †M†±5For every point on†? , we can fi†9the correspondingŽq?”22 so†(atŠ-‘ isŠ= shortest from†ž to C2.\Œ¸8į(†¥-(x+0.45†Ñ -0.975)Ή‰=΋Y“B‹^ (0˜YP† `€„PpB`Š Œ0†  9I)W2†† † v† ††r† Ž A† 'LŽ'Š C˜ u˜x˜yŽ †qˆqˆu9ÈÀ  ŠK5@†ŽÐ6–°†dCfqtŠ ƒ€(g¬ŽGŠ©Length of DA: ÿÿü†ž'ŽzÄÈ ŒqA˜qAw!Q‰ˆ‡ Y™ †q2gFŠ žKœCD˜´—ˆfŠC8#hU‡_ ˜ µV9Ë’û4šû&“”ûvGˆs#q¢ûSlope of tangent at A: ÿÿü††#†&І.††;ÈÈ" Š@†JÐ6–°†QS0RA†\ ™ w7DXyŠ f€ˆVe†.N†F9ÈÀ ŠF3–Gd6a—ˆY ™4—0u˜;˜ªÀDÂÀ ŠÀÀ ¨À—ˆf†y Y™ vcAŠ 8#hU‡4Y˜ŽN œÀ2šÀ”–Ày&c7‰¢À Coord‰€µu‡m†Ž “71@†Ð6–°†Cfqt† SDƒŠ ˆ*ˆ.Ž  Coord of D: ÿÿü†ž%†Ž †n!Ä@  " † †„ÈÀ–Œ vcA†¥ ™—ˆf† Y– ™W–2g”‰fŠ<†ÓŘeˆˆeˆiˆ1šƒˆÚDHŠ•E› ‡1p%‡% —…EiP„†2`˜†‡FÊÀ!”Ø-(íëx+0.45)^2-0.975†H†¢ ‰\‰ ˆ‡‘5Æ@!š¾‡#Ȉ  ¡#†Š’ – 95C†+ ™’1Y– ™&X"xH†O ˜††XÄ@  G †††šˆGˆ†Œ2À˜†ÀH"ŠFB@†®Ð6–°†µ•4VŠ••T“b—9й˜Ñ†œCC˜C&GPŠÌ3G‰ —žCвH–˜ˆUˆÌª‡TÈÈ–µ w7DXy‹>S0RA‹V%1Vgwc‹VŽF¢v‰ˆv‡´Å‹\††Ž†5Ä@  ކ&94x&†1Y™Ž– † ™Q‰‡4r†U ˜†ˆA!šJ†pW–2g”‰f@†!†…Å qˆˆ“"†£.ɘ#†µ3ÈÀ–Ž4ˆ_$¢0ˆˆ4%†8.ÈH!œhˆˆdˆ<ˆ"ˆ@ˆˆˆî1¢šˆPH†–z† ˆ!Žˆ“‘Z–)† † † ††‰Kˆ@‰•Pˆ ‰‹“l\¯Έ'† Άˆ Š ™™™™™˜† `@”Gs Š ˆ.†ŽŠ –DvˆŠK†r† Ž A† ŽkLŽ'ˆxC˜ u˜x˜yŽ †qˆq(†¾.È@ ˆŸˆÊ)†3ÈÀ–*†š-(íëx+0.45)^2-0.975†+‡ ÄH ˆìC@‡Ð6–°†m`ŽÖY™ ƒŠñŠ ˜†,†l”l–Bw‘etd†* ™ „vS€Š !4%8‘G-¢ÒˆÀˆÖ.¢ìˆ±)(†,†.†-†)Ž/†1Å@  † †+†*†HŽ 0†>ÄH–"1†PÈÈ@†_Ð6–°†fhW„p˜‘†q Y™ …h‚6&Š ‚€!‰€†‰Y—†32†TÄ€¦B %a1† –T!G†" † †3†Bʸ4†–†–`†‰B–—ge(Y•Š™—#†XxŠa˜<–ÙˆÝ5Š]˜óˆ]ˆµˆ6Š{H!’7Ž{Š{™Y9ip‡‰ƒ ™‰‡žz8‡£ ÉÈ ¥S ƒ—8E1I ™x1(G’d† YŠ HІ9†!ÈÈ `† @†0Ð6–°†7Œ*†Aˆ6`&GŠ" ˜Š)Š.Š7†:†gÄ@! ˆX8†6mhŽ"ˆˆˆ22†*†Ž ˆˆ94†1†+†,Žsˆ-Ѝ [†â -.3593914697’ 9832099058Ž',ž5 1783128480Ž 0.0160261547R‡<Œ`"define g(x)=-(x+0.45)^2-0.975RŽ)done[Œ•–Asolve(x^2+(y-1†;=1,y)Š:ŽÆy=-ŽÒ -x2Œ+1Œ +1,y=Žª,’5RŠEŒLdefine f(x)=1-Œb 1-x^2RŒ'doneŠ8Œ diff(g†5,x)Š(Ž|-Œz20î’x+9ŒR10[Œ¾*We Žuthˆ rivative of g as g1 below:˜© Ž©g1ˆªÄn¶½g1(c¸¶cÞ¶fˆ¶fš¶ªdefine f1(x)=diff(f† ,x)RdoneRˆ ŒŠ.Š!Œ"xŒ,-xŒ72Œ?+1–=†k0.5Œ`Œb3Ž3ŠgŽX g(c)-ˆ’ŒŠc-xŒ” *g1†+1=0ŠªŽ‚-c+£9Œ–20 ¡-¼¿ŽÜL7M40øî’Œ820î’c+91†Žx-cSŒ¹Ð싟˜ìPî’c+Œ 9Ž20Œ 2Œ%-0-x +1ŽML7M40Œjx-cuî’¼PŒ +1=0[†±Ž§ g(c)-f(x)ŒÁc-xŒË *g1†ˆ5Ê.f1†Eˆc {x,c}[R‹‹# &solve(((’z)/(†v))”q ,c)RY8000î’c‘K3$ +10†–23 -4Š4‡)î’‘¡ŒH2Œ+1Œ-24660Œ -3600î’Ž-x®; +7839=0[Œ[Rˆa– \Œ{Ј;† ÊŒ N&L%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡Ìxy†^‰Ø<†U†y2‡ †³8†i†ä†€L´ä<‰TŠÈäŽP †W †ä† † ‡np’Š©†Ý’†Þ;’”’’ ’’¬’’¸’’Ä’’Ð’’Ü’’è’†ô†ðŠùŒ ‘ †!‘ˆ¾†"‘,$†#‘@0’ˆ‹W<†%‘hH† &‘|T† '‘`† !(‘¤l¸†ä)†x†  †*†y„†}+††,†œ†-†¨†.†´††pÀ†1†̆2†؆3†ä†4†ð†5†ü†ÉEð†F†Ê† H‘ † I‘,ˆú†ÓJ†Ê8†K‘TD† L†ÊP† M†Ê\† N†Êh† O†Ê t’ˆF†Ë€††Æ†Ú Q††Œ†R†ƒ˜†S†¤†‰°†]‡h ¼†i ˆ^ŽÐ_†Ć‰,ȆaŽàb†І”†Ô’Œ•†à† ͆ì†Άø’ˆZ‹ ’ב,† Ø‘@† Ù‘T(† Ú‘h4† )Û‘|@‘ Financial‡ª Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡X‰c ††† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è†]–|œš"˜| “i™” ™‰G‰K† &“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´ˆ²††°† Š” †#’$†(œ†AŠ +†V! 3x(-(-4*x+4*(-x^2+1)^(1/2)-7Ž )/†/2’O(Œ<Š<º:Ž9†›Ž;`– PÎÆ$´$“– –0” – •%i™`‡e —‰@`Y†Û# ™˜<™€(1…0qy`‰X#Y‡uYƒ‡­ ˜–‰»‰ ‡ƒ;Ž ˆ – ˜Æ$ÊH’ ’¤È%°´þaþ þߞجð`@» —’e5‰y`” – œ†ˆ$†Xˆ \ŠΈ<† Έ† Š/Š™™™™™™†`V%Œ6† Œ˜† –˜DvŒd†K†r†  A† ŽkLŒ‹ŠxC˜ u˜x˜yŒ¿†qˆq=†äˆ@  Œ -íëx^2+-1†>†ˆ!Œ@‡Ð6–°† Š÷4ŒÖ– ׈GˆjˆˆŒâ[O[Z)(step1: construct two curves, C1 and C2. Ž0 step3: fix the curve C1. -ˆ 2: construct a tangent to† Œ1 at C2. Œ6LŽV˜6perpendicular lineˆAˆtPІJ a given point‰NˆS4: sele††ˆ¬inters† ion betweenŠÅnormalŒdand†Ï (**sometimes we Ž©can†/t‡nd‡ is using CP)zQˆz 5: animateŠbŠ› (which†O•eˆFœÓ) along‘[‹'(J&step6: collect point C Ion C1) and theŽA ˆ2 afterŠanimation. .ˆQ7”QonlyŠB x-values for†aˆYA. Œ6Ž>7T†lfirstˆ’umn=x Š7Šy1 (wˆ †R concentratˆ ŽH/”¬that isˆ²low†¯half ofŠÏcircle´&ˆvseco†íŽw –x‰C2–¬2Œð -0.7526798709Œ†25´ ˆ4 2397959184´Hˆ\22Š&367®p -0.2193877551†Š 8324367047”20918†35”( 745403719–1989795†-”P 680830956–<18Œv02”x6256758†}”Œ 1785714286” 576195262–´16Šž469”È53064†64”Ü 158163265–d 488014869–d14ŒÆ3— 447671078Ž †d13¢Ç4‡+62†;—S12Œí0–‹ 372157965˜Ÿ1ŠÄ38—?33640429“?-0.1071428571 † 3016986366Œ†( 0969387755–) 2678748608–)86734ˆ-Ž †f 234792892–( 7653061224”z 2023324919–)6632Œ,”£170†Ž6503–)5ŠN489ŽzˆÌ138†Ê818Ž=ŠÌ 4591836735”{‡ 674392˜{3‡™޹7393579˜|2‡0204‘ ‰Hˆh82957ŽâŠ)1öŽ|325995ŽS-5‡šŠO16îìëŽç ŠA28260†W5.102040817îìë3ˆ 0.04593284732” 1530612245Œ †( 766890038”'255ŽV’'1†(236359”' 357142857Žb†N1388125†bš‰183673”u 1703357756”°5Š™489Žu 0.20227979–M66326ŠÆ’t23†å9217–M7Œ$22”é 2678199907”'8†–46938”é3016423†”'9ˆ#†®5”u3‡ 46385r#”› 372098048”®11’s 0.4090998654 127551020” 4476058565Œ 0.137Œ'’8 4879460267”K47959183” 5305682809”q 581632653’„5761†971”&68367346”962558†J—†9 1785714286’˜6807†u7–_188 ¾745†•16–ö19†ŠÀ’¾ 832236188”˜20ˆá673”…¨&193ŒtºL2/—C¢r0.2397959184 0.8322361881Œ†&5\Œåˆ?† åŒ LN SpreadsheetSІˆÈ †ä†† 2@ˆ † 2@†Rg˜p†DY™¯á´´Ò62Cgp¬lE@7Pª‡€ƒ V®%gX$0ª½vRbªØ0d†‡¦óˆHi`«Ggx¬½ !ƒ¬lrye”l@6@B–PY™¯áši†6`ªg‡H`€ª64y(’ˆP¤Q3$‘ªlp8vP0ª‡8†8ª¢gC’¬Qg95yŒQ˜žØY‚•tŒ¢ S2Y•¬6R‚`•pˆ ¤Q2„s ªf‰8‰^¤6b65н ¡z8%"@¬p3Wu` ™¯á@'—”ˆ¦4s’®6g™pªQd#†®64c…0ª‡r €Hª¢ ˜e@ª½G`XVPªØ‡”`&¬¢0V‚€«vX—¬‡%X€–¬l€su¬ØE(`¬½2#aˆ¬ó¬2#aˆ ™¯á@´¬2˜9PˆPˆY T9yY@¬)Y6p¬68wUŠo¤Q 6sŠp¢l˜—•‘€ª‡ˆ†P ª¢xW(`ª½h6sFªØX2e0ªóG•‘ƒ¬Ø7uQ‡„©)'U ­)4i8ˆØY™¯á@(W¤ i8wUŒ˜ž6g4i8€ªe0a"@ª6c&S¬Qa"D‰¬QY6sPª‡W’½ ¢U @¬¢S$¬Q†5`Š—¨pˆ  ”Q ¡)”‡¢н ª6”ó Q"a"D‰€ ˜¯á@c&Sªe0a"Pª6g4i8¬Q i8wU¬Q(WŒ™ž‡’Q¢'U @¬67uQ†ÄªQG•‘ƒp¬lX2e0¬‡h6sF¬¢xW(`¬½ˆ†ò ¬Ø˜—•‘¬Ø 6s_¡“D‹)@)Y6p ™¯á˜9yY@¬Pˆ2”62ކXˆR!7c† `7 ˆ %>Y™”  ™†“kˆ'a” –Š—[ˆ¹\Œ(6Look at when x near 0.5, we get c about†10 somethingÔˆFˆèÊŠˆ£DN&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°h† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡–  ˜9“˜†Ì Y™ ˜p4w8†Ø ™–„”x@…$†ñ —’Y†ª4œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH2#aˆ‡ * ™PˆŒ ž¢;– àHàxਚ2Œ¸†¼‡†ë$s<†H†T†`†l†x†„††œ†¨†´†À‡«̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆa@† LRg˜pY™– – œ2CgpŽ0E@7PŒ<€ƒ V %gX$0ŒTvRbŒ`0d†@ŒlˆHi`ŒxGgxŽT !ƒ†Crye†K86@B–Žli†6Ž<g‡H`€ŒÀ4y(’ˆË†Ì3$‘ŽØp8vPŽ8†8ˆXgC’üg95yŒ´˜Y‚•tŒH˜S2Y•Œ<˜R‚`•Šü †$2„s Œ f‰8‰C†b65ŠT ™8%"ŠÀ† p3WuŠ´†'—”Œ0™4s’g™‹†-"d#† 64c…ŠÀ ‡ €H‰P ™ ˜e@‡4ˆ YG`XVPŽ ‡”`&pŒ0V‚€Œ$vX—Œ0%X€–Ž0€su0ŒHE(`ŽT2#aˆŽ0– ®œ2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†oø(4@L‹XˆØY™9yY‹ † )Y6‹h†8wUŠü†$ 6s‹\Y™˜—•‘€Œ<ˆ†# ŒHxW(`Y™h6sF‡a'X2e0ŽG•‘ƒpŽ$7uQˆ/ˆ0'U @Ž<4i8€Ž‡_ (WŒT i†l!Œ ˜g’$˜e0a"Œ<˜c&SŒ0˜a"D‰DŒH˜Y6sPŠœ˜†§ŽT˜ˆwŒl˜S$Ž$†ŽŒÌ—Š Š´ —”$ –< ŒT Œ”l†„†œ Œ´ŽH”Ì ˜”äˆ8ü —† “,†“D†$“\†0“t†<“Œ†Hx‘¤†Tˆ†kŒ´™˜—•‘€ ™ ˆ† ˆ 8wUŽ )†¢#pŽ9yY@Ž$Š,Œ0 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†Uø(4@LRg˜p‡#Y™– – œ2Cg‹0†0E@7‹TY™€ƒ V %gX$0ŒTvRb‹lY™0d†‹`Y™ˆHi`ŒxGgxŽT !ƒŽ0rye‡ Y™6@B–PŠ i†6`Œ g‡H`€Œ4y(’ˆ#†03$‘Œ0p8vP0Œ<8†8ŒHgC’Ž$[g95yŒ$˜Y‚•tŒH˜S2Y•Œ<˜R‚`•pˆ  †$2„s Œ f‰8ˆ›†b65ŠT ™8%"@Ž p3WuŠ´ ™'—”†w™4s’g™Œ`™d#† 64c…ŠÀ†*r €HŠ  ˜eŽ`†ö`XV‹ †F‡”`&Œ¨‡V‚€ŽvX—Ž<%X€P†h€su†43E(`Ž´2#aˆŽl– ®œ2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†ð†wü ,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LP† Y™9yY@Ž )Y6pŽ8wUŽ$ 6sŠ4Y™˜—•‘€Œ<ˆ†# ŒHxW(`ŒTh6sFŒ`X2e0ŒlG•‘ƒŽ`7uQŽ„'U ˆB4i8`(WŽ„ i’˜g’$˜e0a"ŒÀ˜c&SŒ´˜a"D‰Œ¨˜Y’À˜†§W ˆ´Y˜U @€Œ S$PŒ†`Š —†pˆ  —”$ –< ˜†© W ŒY6sŽ$Š[Ž$ŠlŒ<Š~ŽHg†¡† i‡Ž$†TŒ ™’$†'ˆyŽˆÕˆËˆ$ˆæŒ¨™ŒøŽ<‹ ŽH"x†©ŠØ†Tˆ†kŒ´™˜—•‘Ž` ’À™’†J)†Ù™9yYŽ„‹4Œ¨ ˆŠõ¦`‹d\’e5‰yˆ” – š†ˆ Xˆˆ[Š Remark: Show this anlytically. Ž' ˆK Example 2.\ŒA (x+2)^2+(y-ˆ=4ΈuA†gΈn† ŠˆŠp(Xh†† `s‘hƒ@†`%ˆ‡†Sˆ0†йDvŽÂˆr† Ž ˆrŽkLŽ'‰C˜ u˜x˜yŽ ‡-ˆqB‡=5ÄH! ‘7ˆJÆÈ  D@†Ð6–°† “‡uQ† ™uˆPG†$`†(†ŠŠD†9ÈÀ   -íëx^2+-2ŒCŠCˆIŒ<Y™˜D2f† ˜†E†ˆ2À@–OF†š@HŠaEš¤PUA†¼Y–I†Ç ¤G†ÝAHŽCF˜ç •&E‰ˆÆ Y•˜P9¨CH‡ Ř˜ˆUI‡6ˈ# Š—?’;`” – ŠdJªXK‡U•U–° 26‘tp#‹HaPuhGˆ› ™ 6‘q ™†G† L† Å@  † †F†I†M†'Ä K–"N†I!ÇH–"O†[ÈÀ@†jÐ6–°†qaPuhGHŠ| 26‘tp#Šˆ‚––QC†.†˜ KW–2g”‰fŠ@P¢¡ˆ,ˆ‡ˆ‹Q†q.ȘR†3”ƒ†DŽ4ˆS¢0ˆˆ4T¢Jˆ4ˆˆdˆ<ˆ"ˆ@ˆˆU‡!1Ä@!œ2ˆPˆæV‡fÊÀ– -íëx^2+-2–•Ž ˆ0¦ˆÚ‰a‰i‰¥‡±2B††† [2† -3.044445151Œ-0.5 2.887509543Œ † 4897959184”'76420461ŽŠ'Œ%367”N6585292šN6938775€ˆN5†N1653Ž:Š'ŽL3–œ47801798˜œ’”Ã3†¯82899–'Žs02”ê 322826416–'28571428ŽˆÃ25164573˜'Šæ346Žb‰8183†b61˜u08163265ް‰_11870707—8ˆ¯‰^þ -2.056039352 -0.38775510’ 1.995448424Œ ˆ&Ž%0ŽŠ'3666736Ž:Š'†469388”N 879471899–'571428†”u8236707›ŠuŠKˆŸ”œ 769098183–'vŽbˆÃ71†ê9076–'26530612–ê66307†ìŽaŠ'16Ž*”N61137841’¯†'ŠJ44–t‡\415šÂ295918‰Œ †M‡l090‘I‰]‹ ‹”M4‡©1179Žû -0.2755102041 -1.41099718Ž ˆ' 653061224”' 362067023–'ŽM08”N 313445597–N 448979592”N†b05986ŽaŠ' 346938775”N216838†+–'’O”N†&71153˜N14285714ްˆê1206093aŠ'ˆ¾1632ް‰0724616”¯0.1Œ™5$ †M0241976ކ‰618367ˆÅ–Õ97574443š(Š%†ê7ˆÖ92‡[6‡<—_ˆ—‰­ -0.8779634832 † 1530612245” 8284726494–(42857†9”< 778463228–<1326ŒS”P72783725šx†s489†‘”P 6764867528Œ †´1Ž)Žˆ; 624291512–³ 1020408163”O†¯11451Ÿ‡ 0918367346–È 516798247˜)ˆLŒË•-46115†¦37–)‰‹–{ 403965459˜)‹gŠô•W34‡f4698ŽŠ)5’Ψ-0.2837326024†040816†53Œ ˆ) 198329558” 0306122449”( 152505707˜Q2’S– 804638348ŽfŠ1’,Œ-9.950126459îìë5Œ¨0\Œ± scatter plotÔˆÅW†ÉʈÏ|N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– 4ˆyqYtŒx3Pcp‰†Ù ™–„!—’G †ñ —’éY–$œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH •&E‡ %Y•ˆˆ Žœ¸†’ – øTøÊÌ2Œ¸†¼‡v†â$j<†H†T†`†l†x†„††œ†¨†´†À†̆؇ªä †ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆx@†LDE`ˆu T0Ž vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A`ŽT%Es 7ua$‡``95 Œ„™THBŽx“fg6‡”q†L‚6pu0v˜Ž´qV Žxf0tHPŒØaxAŽäV’<Qˆû†üFy0A —6 gˆ14EYކ)&PY† !h8Pl‡S8 7„$aiäA—i†’ utD6‹8Y™ 'a4‹€† w–4ƒ‹†(G&I‹Œ†xF2(ˆØ Y™'ƒrS ‡- † vHgR€‡-$)PŒAqE y‚GŽagcpŒ<–TYŽ D”F˜ŒTƒs&@Œ`ƒ)UŽ`RPW†3"cƒH0Š„˜ •&EŒ<•2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†aø(4@L‰c‰g‡t‰yY† 6‘Di8wUŒY6s€H—•‘˜ˆ#°(W(`Y™†"FŽ 2e0Œ†+ƒpŒ$‡uQˆ/†0†N @Œ<g4i8€ŒH†SW‡yF“‡uPŒ`†_“Ž`&S ŒxˆkŽ„$IŽ`†wg†…qB…Ž„† ƒŽ`e0a"ˆˆ†.D‰yYŠ.›w†>"$H—•Žä(WŽäˆñŽä†³QŽäƒ†Ùˆs†Íˆc†ÁŠË$ˆ B†©D‡Baˆ "†‘h$H˜ˆ4ˆyh •€˜‹˜˜”¨˜†Á¤˜‡~` Y˜2e0† † ŒÍ)†ˆˆ`Œˆ Ž$ŠŠ$’ ” 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†$ø(4@LDE‡ #`ˆu T‹$† -vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A‹T†:.%Es 7ua$‡``95 Œ„™THBŽx“fg6† †lT‡”q‰Š ‚6pu Ž v˜0ŽqV `Ž$f0tHPŽ0axAŽ<V’<QˆSˆ`Fy0A —06 g†s014EYpŽ„&PY†@Ž!h8Pl‡S 7„$ai´A—i†– utD6ŠØY™ 'a4ŠÌ† w–4ƒŠä†(G&IŠl†xF2(Š('ƒrSŽ$vHgR€ŒH$)†²qEŽ0y‚GŽ<agcŠÌY™–TŒˆd D”F˜Žƒs&‡Aƒ)UŽ`RPWŽcƒH‹€Y˜ •&E‹¤Y•2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†_ø(4@L† Y™‰yY@Ž † 6pŽi8wUŽ$Y6sPŽ0H—•‘€Ž<ˆ# ŽH(W(`ŽT†FŽ`2e0Œl†;ƒ†‡uQŽ„† j Ž„g4i8Ž`†SWˆF“‡uˆ6sF“†@&Sˆ0ˆkˆ.$IŽä•‘ƒgŽ„…qB…p ˆ®Y™†Z Ž e0a"@†ªU @€†ªD†Â †ª†jwPŽ<$†³†¬†­0†¬†¥pŒ`†{Qˆk†lƒ†—†¾s††Æc†‡Ž„AS$Ž`B…qBŽ`2†Ž„"†‘`ŒÀ$H˜`ˆyŽ„ 6sFŒœ˜†Že0Œ0˜”¨†djH—ŒÀ˜†ïŒT˜ˆ¿eŒÌ˜†IŒÀ˜ŠØŒx˜–lŒ‰O Ž ’ ‹a¦`ŠÈ‰Œ —’e5‰yˆ” – š†ˆ Xˆ†[Š Ž Example: Another eŒ Œ)\Œ1 animationΈˆQΈVŽ\ŠwVYrq’† `9ef‰•Š ’G5‘'† @ˆ™Š ŽDˆ³v’K†r† Ž A† 'LŽ'ˆçC˜ u˜x˜yŽ ‡Y†Æ@  † †Z†ÁH"ƒŠG@†&Ð6–°†-D‰X’BE†& 4u„g€†Š <Ž [†Y ÈÀU–B%‰‚ƒ†z ™ t'pˆ` Y™•xaF23ˆ’™†3\†BÈÈ ƒ`Š…E˜…Ph¶†Ož…]†ÞÉÈ ŒCF˜È”7˜ùŒz˜C^‡!Ä™ˆ˜ˆÞ_‡;ÅH–ˆoˆ‡TˆµÇ¡Ua†‘ÉÈ!¥@"p„‰™h!G !R‹"77#5ˆ¢‹dˆFbŽ”†F†c†ÈÈ ƒ`ˆC@†Ð6–°†€Ž%` Ž  ™’ Œd†C ÈÀ! Š–B)€XB†6 Y™vuWHq•Š 4V3Q1І3]މe†•Ä@ ŽJŽˆ`b†1Ž"ˆ_†^†[Ž$fŠ:H–:\†gŠšÈ–Ü h€†0ŠÐ)#IX–ŠÜ&ifH49Šô†h"D™EDP” Ÿˆ‰i¢ŸˆYˆŸf Ž"ˆˆ.j¢Íˆ.k‡² ËÈ#gÐ6–°†R2—X€b† Y™ 5‡Y!‚‘† ™Gd‰T˜†*`†.c† h†l†;ÄH  † †Œk†QjÿÿÿÿŽ"ˆˆ.ˆm†m5Å@!’2n†DÄÈ ŠDA@”Šn†&6†¨ƒ?†½o†ÂÊÀ!”‡-(íëx+-1)^2+-4˜H«ˆ×PC yHqyHr‡  ˆèp‡Ç@–Ûq‡(ÃH©B¤©–©ˆ ¢©a†ˆbÇH–­ˆYs†ÃÊÈ‘—h!G !ˆª ™@"p„‹” V ”t…†q† t† !Ä@  † †s†aW–2g”‰f€†u†4Ř'n†a††v†R.È@ ’w†d3ÉÀ!”oŽ4ˆ_x†‚.ËH–0ˆˆ4y†œ.ʘˆ4ˆˆdˆ<ˆ"ˆ@ˆˆz†š1¢šˆPH–vžƒˆ·‰c†h†k†\†g†]†[†d†Z(ˆAm‘$ [(‡L -0.5229403823Œ0.8” 3946122586Œ 0.8179487†”E 264952635Ž;ˆ'† 97435ˆ' -0.1338658196† 0.8538461†Œ-1.252210698îìë3”+71794†Ž+†> 1329899095”Q 897435897’d 268966744”& 907692307”&4067†ž94”9 925641025ް 0.546562241’Â9Œn43”Õ688409†˜4’„9Šäˆê”û 324496012’ã9Œá7–Ð978805‡•49âŽ_ 1.1276045- 1.0œo†2789807‘iˆ$3333†”643‡006ޏ 1.051282† 1.590014988’ 069230769’$74996129”6 087179487’H 913061434’Z1mŽ2.0†372246’~1Œj23’$24935616”14102564~ 2.42288213”´15897435´2.600†j522’ê1Ši07´ 2.78156478¢1.1ˆÔ†Ú”´96709031”´2CŽ´ 3.156‡!’é1.Ö³ 3.3514836–³2Œj4³3.55‡v341”26666†‘g3.755053048 1.284615385Ž 3.964578506’$ 302564103Ž 4.17957508”H 320512821’$4002871˜H3Žm’H62696877~1.3Šj†p’l85988425Z 1.374358974Ž 5.099308679’Ø 392307692’$34552861Ž$ 1.Œi4Y5.Œj33”k428ŒÙ’k85956060”³4B4³6.‡ 00†¥‘11.4ŽÖ޳ 6‡45209•f4Žj² 6.68945373œ 1.5[\ŽÔˆ{† ÊŠ¨N&à%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H„ ˆ^<̇P_PP†iŠ`dˆZ†faxˆãbŒ\† d †FŽde´ä†”Èh’´•Üt†Íð€†ΑŒ† Б˜† ב ,¤’Ø‘@°† Ù‘T¼† Ú‘hȆ 8Û‘|Ô‘ Financial‡ªForma†¾ †††Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– W&DŠx8–Š$–„B˜9UW†ñ ˜pê ™”`˜0™ (1…0qy`ˆä#Y‡uYƒŠH–˜œšH®Æ$ÈH%"i€‡/Y—qyHqŠ  ™ˆˆŽœ¦’ – àHàxਚ(Œ¸†¼‡~†ê$r<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Oü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDtÔ"”‚0‹ ™”a"X`‹¬™d•&5‡¸ Y™3†X`Š %"i€Š —2˜™ Pˆ ™h–gDŽ xe”pŒFV"Aˆ;†$ˆ@™@Œ02D– Œ< x€QŠ`†7UvSˆk'‰€sŠl† C0pŠ<†Y˜t™a)Ž$‘0aCŽ$”r$Š´$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÌˆ$–p1Ž<i–Ž5ƒcˆ$UcAŽ0uPSލ–ExPŽx•uŽÀ@‡†0ObihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ( † ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ†£0 ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i#†}%d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( QŠx †P#†ˆо $‡”†¹&fffpŽ(F8PŽ$0†¥0Ž02†u<3ŠÑH5ˆ»ŽT7†»@Ž`9†m ŽlAVAˆwˆxB‚†DaS„&<F†%<H Q(<ŠŒŒ´ (†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ"”‚‹DY™”a"X‹,† d•&5Š3†XŽ%"i‹\Y—2˜™ ‹Œ ™h–gDP ™xe”pŒ FV"Aˆ†ˆ@™@Œ$2D– Œ0 x€Q`Œ<vSˆG '‰€s€Ž C0pŠ<†Y˜t™a),Ž$‘0aCŽ$”r$ŠT$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÀˆ$–p1Ž<i–Ž5ƒcˆUcAŽ0uPSލ–ExPŽxg•uŽÀ@‡ŽbihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ(† † ††$†0†<†H†T† `†$lx†)„††œ†¨†´†À†̆؆ä†ð†Nü ,8DP\ht€Œ˜¤°¼ÈÔ† ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i# %d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( Qx#†Ùx$‡”x&]fffx(F8 P0%d0Ž 2‚Ž3„aS€Ž$5d%`Ž07CX—@Ž<9#i ŽHAVAˆSˆTB‚<DaS„<F†%† 6H Q(<ŠŒŒ ˆ®`VŠi†Í ˜’e5‰yˆ” – œ˜`†‰XˆŽ†’[Œ eActfH x1-à(1-x^2)f1H xà:(f(x),x)gH$x-(x+0.45)^2-0.975g1H(x((-(20*x+9))/(10))h1H@/x((-à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))h2H@.x((à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))020010distance06-3.EAC010000001983É distance06-3.EAC† main.ACT† †#†-ˆ0†4ІG^E ˆŒ'[†4ˆ7 Example 1ˆs ††|+)Consider C1:y=(x+1)^2 and C2: y=-x^2-1. Œ9'For every point on†: , we can fi†8the Ž_correspondingu(”;2 so†1atŠ6‘  isŠFŒ­shortest from†© to C2.\ŒÃ†º†¨» ºΉ‰/ÎK‘4‹P (0˜Ye† `YdG€D Š Š'‰£‘@v"p‰¯˜Dv†ˆr† Ž A† † †"LŽ'Š C˜ u˜x˜yŽ †c† †Å@! ŽuŠÄH"ŠC@†ŽÐ6–°†•WC6Gi•†  Y™5r…†  ™˜†C†ÁÈÈ ŽU–B (F††cˆá Y™qA†6dŠ q–QqBˆò1Æ¢—‡ÉÀ–­ (íëx+1)^2†H–'†Æ5Ä@ƒ† ŠØÈ ŽØA˜Ø‹j‹v†ØˆCŠ`’Ž  ‡™Êš€-†€^2+-1˜C†Š’ Y™2f†Y˜† †(!Ä@  - †:ÈÈ"Ž@†IÐ6–°†PqA†6dŠH (F††cˆT ™‘2R–‚Š †x W–2g”‰fŠ@ †Ře Ž–ˆš†«.ɘ†ƒ3ÈÀ– Ž4ˆ¢0ˆˆ4†8.ÈH!œhˆˆdˆ<ˆ"ˆ@ˆˆ†š1¢šˆPH–vžƒˆ·†f2ˆ!“s[‰ƒ)(step1: construct two curves, C1 and C2. Œ/!step3: fix the curve C1. -ˆ!2: construct a tangent to† Œ2at C2. –4†U˜4perpendicular lineˆ?ˆsŽjWІQ a given point\+ˆ\4: sele†ˆ´inters† ion betweenŠÍŽÃ#normalŒuand†ß (**sometimes weîcan not‡nd‡ is using CP)‚#ˆ‚ 5: animate‹7Š£ (which†O†ÔŽQ.“8eˆPe“<‰) along‘u“@.%step6: collect point C on C1) and theŽ A ˆ2 afterŠ animation. Ž#.ˆY7”YonlyŠK x-values for†iˆbA. ŒX Žb(T†vfirstˆ›umn=x Š8Œš (wˆ †SŒ‘ concentratˆ"…/”¼that isˆÙlow†·half ofŠßcircle’¼&ˆ}seco†þŽ~ –‰ C2. 2-1.902673945îìë4*0Œ -0.05031899979– 1020408163–* 9302125331–*(27† -0.1357235068 † 0306122449” 1784257604Œ†< 04081632653”= 2164864646–)5102Œ.”f 2526905491–zŒx89–Ž 287223675ŽŠQ714285†–z 3210141547–)¡0–z3540619†@–)918†e346–õ 385438858™ Ê–ô41607308Ž ˆ(¤Ê 446150323ŽxˆµŽð79—47548491™W1ŽÆ12¨-0.5048195068 †142857†9” 5334114505–(53061224–5†607463–(6326Š,Œ ˆx89110042–'73469387–‹61695933˜1836Š+4”³ 6448086336”c1ˆL755Žvˆc67265792˜;20408ˆ£7”ž70124987–Å2‘–Ù 729099168—=‡489795—=7576†ï12—=2Ží7޲ˆÚ7862830‡D”Ú’O‘*-0.8156176477 † 2551020408” 8456948871–( 653061224”< 8772574223–(7ŽQ–< 911790549˜P85714ˆ”x 9416821266–(95918367–d9760ŠŽ †ÜŽ491.01†Ø801–²3163ŒÊ–'‡3702—Ž$†î–N9373928—3ˆ—4693–u 136441535”׊#87‡”œ1865†t6—Š3‘ŽbˆÃ24412547ˆÖ -0.3673469388† -1.31560533ŽŠ' 775510204”'4†92943†'8Ž(²&ŠM 979591837²Mˆ› 408163265’a¢tˆÂ4†IŒÅ²›ˆé428571†6²Â‰4ÌÃ448ŽÅ³‰^4Šç‡c5³7‰…‹‹b³^‰…476‰8 -1.410292943† -0.4897959184Œ¦'†'5[Œ3\Œ; look at x=0Ôˆ†ÊŠ%üN&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– U!aŠx@‚ˆ  ™–„"A!Yˆ» —’éY–$œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈHA’”0‡$`ˆˆ Y™’ ’¢š’ –HàGàwে2Œ¸†¼‡|†è$p<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆ+@†L&s”PY–™—Š ˜ 0!%3Š˜5r5€†*™xBW`@Š0™Hdd`Ž RiIŒ0™‡"6uŽ0!ATp†T… …CˆXŒl™0„0†1F#Ž0uHIŽ•„3APŒ´™a&FŽ<‰BˆËY™•“7Ž´D€†3ލrey)ŽÀ$˜sŽ0) ‘hŽäWi™†(0V™avGŽÌEiH‡w%t"ŽÀ y“ Ah!&  v•‘†? H‹D`7‹\ˆ  79(‹tˆdAS‹˜ˆep&Œ($A%G‰¤ -`1V3€ˆ A’”0– – ®Þ0Ü`2† † ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†qü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†^ø(4@LˆÒˆÖ‰j‹hY˜ˆ 2pŒ $I‰‹††"2eŽ$ @`Œ0†#H˜Ž$(W0‡"Y˜2e0`Œ  6sFŒŒR)Œ$™$H˜ˆ/ˆ "D‰yŒ0™†;a Ž$B…qBŒ<™S†m$PŽ<c&SŽHsF“‡€ŽTƒg4i@Ž`“‡uQŽ`ˆw†›$Ž ’¨™$H—•Œœ™4i8wŒ´™†YŽ„U†ªŽ`e0a"ˆ"uQŽ„†§…`•‘ƒg™†³IŽä•ˆ ¿ˆ ‡“ ˆ ËuŽäW†©ˆ%†×8ˆtwˆ‘Ž`†ãD—†yŽä‡f†mŽ •€™‡£(˜™8ˆIŽ0‡‘€ Y™Y6sP† ˆ i8wUŽ y†pމ† @Œ$†6†9Š ’ 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†Uø(4@L&s”–™—‹$˜ 0!%3$˜5r5€<xBW`$Hdd`TRiIT‡"6uŽ0!AT`T…l…CˆXŒl™0„0œF#‘uHI† Y™•€Š 3APPŽ a&F0މBˆ#†0•“7Ž0D€†3`Œ<rey)@ŒH$˜s†z6) ‘hŽ`WiŽ`†(0VŒxavGpŒ„EiH‡w%t"Ž„ yI†³! Ah!&Žx v•‘ލ HŠ„`7ŠØˆ  79(ŠlˆdASŠäˆep&Šx†(;$A%GŽ<1V3<A’”‹– ®Þ0ê`2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†Gð†uü ,8DP\ht€Œ˜¤°¼ÈÔ†à†ì†@ø(4@L†Š0ˆY˜ˆ 2pŒ $IŠ)†!†"2eŽ$ @`Œ0†#H˜Ž$(WŽHŠ/† 6sFŒ`–l™”<™"D‰yŒT†?†ja Ž$B…qBŒ<™S†‘PŽ<c&SŽHsF“‡€ŽTƒg4i@Ž`“‡uQŽ`–Ø™Ѝ ˆ¤Y™$H—•Ž 4i8w`ކ^Y†VU†• €Ž0e0a"@†UuQˆU†m…p†U•‘ƒg0Œ`ŒÏ ˆk†l2e0ކ†ˆ†º“Ž„†‡uPŒœW†Ù*Ž`g†Ž„wˆ‘ŒÀ‡†…`—†yŽ„ˆmŒä†aކ(†Uˆ 8ˆI‡‘ˆY†1Ž„†Šy†Žä†‰KŽä’ †’ ‹%¦ `Dh'Q8‡ —’e5‰yˆ” – š†ˆ Xˆˆ[Š Remark: Show this anlytically. Œ&eAct020010distance06-4.EAC010000002e4eÉ distance06-4.EAC† main.ACT† †#†-ˆ0†4ІG^E ˆŒ'[†4ˆ7 Example 4ˆs Œ")Consider C1:y=x+sin(x) and C2: y=†š†. †I†¬5For every point on†; , we can fi†9the correspondingŽm?”22 so†(atŠ-‘ isŠ= shortest from†š to C2.\Œ´+†«†™’¬(thick),š±Šn)Ή ‰,ÎH‘7‹M e…˜† `8 €Š vy2†‰ ‘—‰¬D‰¹v†ˆr† Ž A† † †"LŽ'Š C˜ u˜x˜yŽ †c† †1ÅH  ŽuŠÄH ŠD@†ŽÐ6–°†•XV‡5†e†  Y™'T'&‰†2`˜††ÁÈÈ …’U íëx+sin(†)†HŽÖÄ@ {†<ÈÈ"Ž–~™2•h0ˆ Y™ €tGTsŒŠ80b#2ŠŠŽF‡C5Ƙ\ †éÅÈ!ƒŠéA˜×Prˆ×ƒ2q2(MŽ>Š ‡˜ÊÀ!•,taŒÓ˜BP†`  @c(† ˜† †&1ÅH  # †8ÆH ŠC@†HÐ6–°†OXTg—S†Z Y™'˜8WŠa˜†ˆ!H† †ƒÇ¢]Že†1š†³Ä’{B˜{W—€7pŠÐw”ƒ††á˜† Ž{†ØšØˆ]‡ÈÈ–Û €tGTtŠÛ™2•h07†  ™$qdEˆ\ŠÛˆF†\!š\ˆXˆ¢ –2g”‰f€†Šƒ@–' Žþ‰‡Ÿ.ɘE†3ÉÀ!‹ † †††.É@  † †Œ†ŠH–ˆ4ˆŽ<ˆ"ˆ@ˆˆ†\1Æ@!œ2ˆPH†–zŽ ˆ‹†† †ŽŽ2ˆ)›[†Ä*(step1: construct two curves, C1 and C2. Œ/ˆ/ 3: fix theŒ)†'. ŽP-ˆ!2˜Pa tangen†Zo aŒ[ at–ULŽU˜4perpendicular lineˆ?ˆsNІHa given point. ÙQ.step4: animate the point (which we constructedŠ tange†"line) along curve C2. NˆX 5: selectŠW†Uers† ion betweenŠpnormalŠO†ˆd C1 (**sometimes†ƒ ŒVcan†/t fi†(this using CP). Ž{P**Note you neˆ´o zoom†ŠßgraphŠˆN”¡mŠ}† n chˆãˆ9‰ŽZdrawˆu tool. With‹7obj†ësŽó‡,ŽOPˆ. active,ˆCˆ@kof 6™$.öI%step6: collect point C on C1) and theŽAŠ2 afterŠanimation. .ˆP7”PonlyŠB x-values for†`ˆYA. Œ7Ž?7T†mfirstˆ’umn=x Š8Œ‘ (wˆ †S concentratˆ ŽG/”¬that isˆÉlow†¯half ofŠÏcircle.7&ˆvseco†îŽw –x‰ C2. 2Œè -0.6590109525Œ-1.Ž ¨ † 448979592´Fˆ'3Š%184´m -1.346938776 -0.6590109525Œ †' 295918367¾'44897959”:482885†N”M1Šr551–`33402678”L 142857143”†0605049†ˆL0Œ—3Ž…ˆÀ 931701973ŽÔˆM04081632–À 831908663–Ô9Œ¾184•74‡ 1†=–<Á0ŽÖ‹781290389’×0.8œ'ˆ62234271Ž×ŒŠ67‹ˆ“70.56†Œ320—˜7‹‰¬-0.5220852482 † 7346938776” 4782226074”(6836Š,– 436912818–< 632653061Žd †x3981558˜w581Œ*1”‹ 3605593327”OŒK2449”³ 3241231708˜³9591ˆ¤”d28838Š-”<428571†޳ˆŸ25333954–î 377551020— 218760001–Ÿ’í–Û 1841804595”P2O–ï15029†Œ9—zˆê89ˆÌ¢-0.1157176074 ˆ 734693878Œ†( 08183429752–) 224489796”= 047718910Ž(Š=71428†i43–R 138356003Ž{Šg204†k6327ŽŠ2797869Ž 0.0306Š~9”'54†80968ËŠ¶†K65†.”O 882784841Žc†O1Ž%1ŽÝ†b†Ü3‰15’u‡6‹Ža†ˆ 156741336ŽÙ†L2=7–9 906246461’L‰’r22566‡e3”L†YŒŽç†ú 260247885‰t 0.387755102† 0.2952915828’4¤& 3310315123’9 4897959184’L 367931829”_ 5408163265Œ†„ 405760456’„ˆF†<347’8 444981547Ž8† 6428571429–„6523413Ž9†â69Žä’¼ 531314364”©74޾• 579122322•Œß†ÕŽõ‡@633††44”ƒ84r’86940006’8†‘,©‡-7650‡71”â9“T–_97246461 1\Œ 8=scatter plot shows you the answer: one x corresponds toŠyÔˆN†RʈX¬N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– qaGŠx)…pYˆ –„S‚„D†ñ —”H`”œš0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œœx®Æ$ÈHIrFF‡$ ™ˆˆ Š’˜ °˜<öHây⪖ 2Œ¸†ø‡r†Þ$f<†H†T†`†l†x†„††œ†¨†´†À†̆؆䇪ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆ@† LY RPY™– – ®ž0H(…• ˆH`#4g€Ž –pŒ 1ps`Œl1†cŠY™IR )‰Ž"4'ˆ›†œi‰2 "RHŠlY™x"&@ŒÀ6‘,(Ž`˜X‚Ž<`U“2Žl$1pŠœY™ˆ82AŽHS3•D†LvŽœ„Y P)qIŽÀqvx4)uŠüY˜w‘Œ´˜85`Œœ˜yxi‹ ˜Ac hІ ‚xHA‹ †"98q†ž ™Vt60Ž bFFˆ0™%fƒCˆ ™`$x…`‡)ˆ •)‚€Œ 10‡g“) Œ$vVˆ/†<D˜GPŒ† †R4p† 11Cd@ŒTy#"Ž<3B„Iˆ'”gŽ`ecqŽHIrFFŒ2†0† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†,ø(4@L‹(‰h`D‰yY‹Pˆ 9yY‹,ˆ4i8w‹Œˆ)Y6‹P†($H—•Ž<8wU‹ †: (W0†G 6sPŽ 2pŒ †W @ˆ$Y™ 8wU Œ ‡uQˆ;†6sF“‡ …qB…Š<†&ˆu`Œ‡† ƒg4iŽH2e0aŽHc&SŒ`0a"DŽH†w6Šh§(ŽHˆƒŽ&SކŽH$H—•ކ›‡€ŒÀ"D‰yŽüY˜’ðY˜$I‰ ˜‡e0ŠÀ ˜’´ ™’Ì ™ˆä‹8ˆ’ü ™“Š, ™“DŠ\ ™@‡ ŽH‘‡-ŽHB‡Qˆ?“†IŒœ™†ËY ™•‘ƒg0† † F“‡uPŽ —†pŒ H† €Œ$ †»m=†@Š” 2††ˆ&N$0<HT`lx„œ¨´ÀÌØäðü†v†z† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†"ø†«(†4†@† LY R‹ Y™– – ®ž0H(…• ‡k`#4g‹H† –‹`` 1ps`Œl1†c‹xY™IR )‰Ž"4'‡¾ Y™i‰2Š "RH Œ x"&@Œ6'‘(`Œ$˜X‚Ž0`U“2pŒ<$1p€ŒHˆ82Aކ S3•DŽ`v†*D„YPŒxP)qIŽ`qvx4)uŒ˜w‘Œ¨˜85`Œœ˜yxiŠx ˜Ac hІ ‚xHAŠœ†!"98qŠl ™Vt60Ž bFFŒ%fƒCކ*`$x…Š ™•)‚ŠØ ™1Ž<g“)Šä ™vVŒ D˜GŽl†R4Šð ™11CdŠ8y#"†83B„I†@)”gŽœec´Ir’¨2†  $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LP† `D‰yY Ž 9yY@Ž4i8w`Ž$)Y6pŽ0$H—•Ž<8wUŽH(W0ŽT 6sŠd†`2Ž< †kŒ`Y™ ˆ;Šx Y™‡uQŠ“ˆ 6sF“Š`†…qB…Šx†&’†$ƒg4i†T2e0a†\c&SŠˆ 0a"DŽHyÀ†U†§(` ˆ·Y™†‰ @†³ &S Œ†jŒ$Š­Œ0†r‡€Œ<"†à`ŒHЏŠ0˜ˆ±pŠT˜B$Iˆk ˜†e0Š0 ˜† aŠl ™ƒg4iŠ„ ™4i8wPŒ…qB…ŠH ™6†yŠ„ˆ )‡†ŒT™8ˆÁŒH‰yYŽH@c&ŽH‘†aŽHB†Uˆ“†IŒœ™†ËYŽ•†1ŠÌ ™†ïu†F—†Ž ‡‘‹†À‰K‰O‹1’®–`‹L ’e5‰yˆ” – š†ˆ Xˆ[Š Ž ! Remark: Show this anlytically. Œ0O(1) No† e if we take†0e last row, x=0.8497246461,ˆ&getŠ%answer to be 1.~3Tˆq†t very clos_u† Mapleˆ4†ifyŠž’;*(2) The anlytical† Qswer can be found at 3'yang->2006->paper->distance->shortest-example4.mwsRˆ9Œ?define f(x)=x+sin† RŽ done–0Ž0gˆ0†d¼.\Œ¥f†Ðd gЈ†Êˆ¾àN&%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡-Ìxy†^‰Ø†U†y2’ðä(’´ä<Œ ŽP ˆ| †ä† † ‡f,’Š¡O8’’D’’P’’\’’h’’t’’€’’Œ’’˜’’¤’’°’† ¼’‰‹Ȇ !†Ô†"†à†#†ì†$†ø†1%‘h† &‘|† '‘ˆæŒ(‘¤†  ‡¸†ä)†4†  †*†E@†I+†L†,†X†-†d†.†p†0†|†1†ˆ†2†”†3†  ’ˆ¾ŠË¬† 5†¸†E†ĆF†ІH†܆I†è†J†ô†¬K‘T‰]Œ‰6‹k †M†È† N‘ˆçO†Ç‰6†ÑP‹¸†Ç<††Â†Ö Q††ˆbR†VT†S† `’ˆŠ?l† ]‡Z x†i ˆ^ŽÍ_† €’ˆZŠ„† aŽÞb†ŒŽâ’Œ•†œ† ͆¨†Ά´ŽÙÀ†׆Ì’@Ø’ˆ ŒÙ’ä’Ú’ð’Û’ü‘ Financia‰U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†` †† †P Š” †#’$†(œ†AŠ †V  3xf(x)’+ކgІWŽ`– PŠÆ$´$’ц Oˆ•Tp”x” –„4x&ˆ) ˜ˆþŒ¨R–ª0™<(1…0qy`‰#Y‡uYƒŠH–˜œšH®®$‡†‡ –ˆP†’ ’¤È%°lþaþ þߞجð`‘u †b ’e5‰yˆ” †4œ™°†öX†ú‡]R‡bŠXg†×Œ xŽ|x=cRtanŒ cŒ2Œ+1Rˆ%Œ+.simplify(((g(y)-f(x))/(y-†*(1+†K†^2)+1=0)ŒhŽh-ªvy’v3Œ+-sin–xŒ©î’ªµy’´Žl-xî’¨á”kŽá¬k -2î’xˆÏ’y‘Ž x-=0\KCP can't draw this ‹2 citplotΉr‡v΋|‰‰…‰Š‰–`Œ"Ž †– ˆ† †vŽˆr†  A† 'LŽ'Š C˜ u˜x˜yŽ †qˆqŠvˆ” Rˆ0ˆ‹-solve(((g(y)-f(x))/(y-†*(1+tan†^2)+1=0,y)RŒ@sinŒKxŽ+x-†:yŽ+î’†9Œxš!Œ2ŒA+1ŒSx-yŒˆ‚ЏŽy define F(x†™=Ž-†›¾f3Œ+-†¼’¾î’tanŒ yŒ2Ž-xî’ª,’-*sinLxŒ -2î’x+†e’yŒy+Ž x-yRŒ‘doneRˆ›Œ¡solve(F(0.8497246461,y)=0†Š8ŽËy="Š“ 2.871448345‡H4Rd†ë[Žô JThe above †]ution y=–5 is not t†(†Ž†at we want. Look †† E ?graph below,Š6zero of xc=0.9998732480889ˆ\X†Sneed.\ŒD)graph y=F(0.8497246461,x) and notice that†ere is zero near x=0.999Іʆ† ÐN(èFinaFormÌ$N†Graph2D†ð†& 3ˆ†3 ˆLISTSYSˆ†@4ˆ< Modify ˆA$ˆ<STATCALC hˆdˆŒ< p\ˆx SequenceˆŒ,ˆxSheetˆOø|’ŠŒˆŒolveEqˆˆ´†€bwrôˆ´(Up†ˆ¥ŒtupFLG1 (Š<†Lis†{4D‰ˆPic†xÜViewWindœˆŒ_osve†b‡ ¸xy†^‰‡+.Ĉ<H†ä‡6Œè 䊗‰@’´ä<Š ŠÈäŽP ˆ~ ˆ.† † ‡kR’’$’’0’’<’ˆFŠSH’’T’’`’’l’’x’’„’’’†œ† †¨†!†´†"†À†#† Ì’‰"‹C؆ %†ä†&†ð†'†ü†I(‘† ")‘¤‰®‡¸†ä*† †  †+†2 ,’ˆ Š+8† -†D†.†P†0†\†1†h†2†t†3†€†4†Œ†5†˜†E†¤†F†°†H†¼†I†ȆJ†Ô†K†à†L†ì†M†ø†²N‘|† O†Ä ’‰J‹§‡Q‹¸†Ã(††¾†Ò R††ˆ†S†B@†TŽV]‡R X†U ˆ^ŽÇ_†`Šð{d† aŽØb†l†”†p’Œ•†|† ͆ˆ† Î’ˆFŒІ  †׆¬†‰‡¸‡¼Ù’Ć Ú’ˆZŒÛ†*Ü‘| FinanciaˆÝ Format ††ˆ †† ˆ‹­ †'†systemä]Setu’^äa† _LIST’`Œ’†,ˆ† bŒTˆk`=@ŽŽž¾ þ@þ€þÀÿ¥@††ˆ®Þ0þ`þ þàÿ ÿ`àŠ 8 ÿ@ÿxŽ š!øÀŒÁ$† a‡ MatDatab‡.EAC‹‹† ”¤ÍˆÍ †I —X† †‡ î<ˆxª<Šö^††ì‰ˆ‰†Ø ˆ Œ‘,ö<þxþ´þðÿ,ÿh—¤ ‰b‰L††¼†† †_ Œ ’,† † 0$†@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† )“-ˆ‰F^E ‰eŽÀ‰`†$«d«yŽ †]¬  ˆD†ŒŒ†e†††¨œŽ †B 3xF(0.8497246461,x)ˆKŽ'`– PxÆ$´$’¿– –0” –„—b„XI€‡ ˜`”0–T˜0™*(1…0qy`‰#Y‡uYƒŠH–˜Hšx²Æ$¦H‡ †† Š  ™‡2H‰† ™’’ ¢²#˜T†j$`øTøøÌ°Ø¬ð`f“P’e5‰yˆ” ®ŸŒ†JW†N†[Œ eActFH`Ox,y((-((àT(y))^(3)-àL(x)*(àT(y))^(2)-x*(àT(y))^(2)-àL(x)-2*x+àT(y)+y))/(x-y))fH xx+àL(x)gHxàT(x)020010distance06-5.EAC010000001889É distance06-5.EAC† main.ACT† †#†-ˆ0†4ІG^E ˆŒ'[†4ˆ7 Example 1ˆs ††|Consider C1:y=Ž1-xŽ,2Œ4 and C2: y=-x^2-1.G5For every point on†Q , we can fi†9the corresponding ŒŒ?”22 so†(atŠ-‘ isŠ= shortest from†° to C2.\ŒÊ%†Á†™((†º ^2)^(1/2)¢²Ή‰=ÎY‘B‹^ (0˜Ye† `YdG€D Š Š'‰± ‘@v"p†† † v† ††r† Ž A† 'LŽ'Š C˜ u˜x˜yŽ †qˆqˆuÅ@! ŽuŠÄH"ŠC@† Ð6–°†§RaAŠ Y™#%P'e“†  ™˜†C†ÓÈÈ ŽU–B (F††c†ó†BqA†6dŒNq–QqBˆò1Æ¢—‡+ÉÀ–­(1-íëx^2)^(1/2)†H–-†Ì5Ä@‰† ŠÞÈ #ŠðA˜Þ‹p‹|Y™ˆCŠ`’Ž  ‡±ʈ†† -íëx^2+-1Y™– ” ™2e1†= ˜† †F!Ä@  O †XÈÈ"Ž@†gÐ6–°†nqA†6dŠ` (F††cŒT‘2R–‚Š`†– W–2g”‰fŠ@ †«Ře †ˆ–ˆš†É.ɘ†ƒ3ÈÀ– Ž4ˆ¢0ˆˆ4†8.ÈH!œhˆˆdˆ<ˆ"ˆ@ˆˆ†š1¢šˆPH–vžƒˆ·†„2ˆ!‘‘[ˆ (0step1: construct two curves, C1 and C2. ˆ0 3: fix theŒ*†(. Œ -ˆ 2˜Pa tangen†Zo aŒ[ atŒUŽVLŽV˜6perpendicular lineˆAˆtPІJ a given point‰NˆS4: seleˆÖ†¬inters† ion betweenŠÅnormalŒdŠð1 (**sometimes weÿcan†/t‡‡this using CP)zQˆz5:‡:imateŠbŠ› (which†O•oeˆFœÓ) along‘[—'I%step6: collect point C on C1) and theŽAŠ2 afterŠanimation. .ˆQ7”QonlyŠC x-values for†aˆZA. Œ5 Ž?7T†nfirstˆ“umn=x Š8Œ’ (wˆ †S concentratˆŽH/”¬that isˆÉlow†¯half ofŠÏcircle’´&ˆuseco†îŽv –w‰ C2. 2Œç -0.8522363365Œ†Ž ¨ˆ3 4795918367´Gˆ4Ž&3¸P-0.4387755102 † 8522363365” 4183673469¼(397959†-7¼P3Žv04¼x3571428†¼ †®Šž3À  163265306”´ 995380991–2ŒÆ†ó”´†Û467004–Ü2Ç–  952821610—2Žî08”Œ 916679171–2‰c‰”–  872113046‘¤-0.2142857143 † 8191993842Œ †(1†77551”' 7574667786”;17346†;78”O 687843539–< 1530612245”w†650440–13†Š+” 530030863ŽPŠŸˆL489–w 4423055814Œ†Æ091836Ф”)348546‡ŽÈŠ)‡£252†ñ215ŽŠ) 510204081™53137060–¶†³Šñ4–z051951žz’P‘’Œe9110‡‚¦ 0.01020408163 0.1522768834’ 0306122449’& 252070193Ž9 †M5’N’M 349078573Žˆ'7142†14”t 4414454045”' 918367346”u 5300989961Œ 0.1Š˜898’Àˆª54418”†1326†<†Ä’æ 687911672”1Œ#2…†757534ˆ)”&Š“387”r 8178750522ˆ—ˆ"755Ž©†8 872645334”2¥ 916740”K†½2Žp7‘V0.9529078748 0.255102040” 979457536–&7Ž'1’9 9956101284”& 959183673¸& 3163265306¸L3ˆG46939¸r 357142857º˜37¿¸¾3†øŠÀ7¸ä4Œá†š¹ 438Žt¹04‘/5¹V4Ž—67 0.9956101284Œ0.5\Œlook at x near 0.Ôˆ7†;ʈA\N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°b† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– D€6ŒxG $ˆÑ†0–„rF†ñ —”<Y†¤5 ™˜0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œšx®Æ$ÈH •a(@‡% ™ˆˆ  ™’ ’¢š’ ”HàGàwে2Œ¸†¼‡}†é$q<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆ@† LR#c6PY™– – ®Þ0 ` •8 ‘`Œx yFppŒ$ R‚ g‘q€Žœr0F ލ“„Ž WFgxŽH‡„59ŒÌe@ŽØ0cŽB0U@ŒðHTb…Ž„IRFbŽ`Sp`ŽlQ(V‰Y˜‘‡Š¨ ˜R'hƒŠH †<“0Œ I…sŠT ™ADTŠ„†„ ‰–Š„ ™%DŽ$‡‘rŠl† ÌSIŽ<‡PR†prdS4Ž< tŠ ™ Rxt€‡ˆ yEu6†æ•a(@‘Ä`2†›† ‡«‡¯$†0‡»<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†`ø(4@L‰c‰g Y™yY6pŽ † sPŽ8wU Ž$6sFŒ0—•‘ƒŽ0ˆ#‹ Y™W(W†=†%“Ž 2e0`Œ†-g0Œ$uQŽ0†N-@€Œ<4i8w0†SŽ0“‡uQˆ_†`†_‡Ž0S$PŒx†;ka Œ„$H˜Ž0 †‘Œ˜”T˜†wŒœ˜†GIŒ`˜Œx–  –$†<†T ˜”lˆ„† œ† ’´†’̆$’ä†"ü — —, —D —\ — t —Œ ™W‘¤ˆPwˆIŒœ—‡™p ™6sF† ˆ 8wU Ž Y†PŽy† pŒ$†6†9Š ’ 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LR#c6‹Y™– – ®Þ0 ` •8 ‘`Œx yFp‹xY™ R‚ g‘q€ Y™r0F Š “„Ž WFgx`Œ‡„59Œ$Ce@PŒ00cŽB0U@ŒHHTb…Ž<RFbŽ`Sp`ŽlQ(Vˆw Y˜‘‡pˆ ' ˜R'hƒŠH †<“0Œ I…sŠT ™ADTŠ„†„ ‰–Š„ ™%DŽ$‡‘rŠl†\ÌSIŽ<‡PRŽ`rdS4Ž< t Rxt€Œ„ yEu6 •a(Žœ– ®Þ0Î`2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†yð†vü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@L†Ì Y™yY6pŽ † sPŽ8wU ‡:"6sFŒ0—•‘ƒŽ0ˆ#@ŒHW(WŒT†!“02e0`Œl†;g0ŒxuQ†2 †j@€Œ4i8w0†SŽ0“‡uQŽ´sF“‡ˆ S$Ž´†kaˆ $H˜Žä ”À˜ŠT Y˜ @`Œ †/*Iˆ†0– Š  –$ –< ˜(WŽ$ 6sFŒ†pˆPŒ0™2e0a Ž S†IPŽˆ€Ž$ˆ‘ Œ`™”T™Š­1Ѝ ™U†µŽ0uQŒ`•‘ƒgŽ0†mŽ0†“Œ™W†©ˆZwˆIŒœ—†=pŒ¨”À™8ˆ%ŒÀY†ÙŽ´y† Ž0‰K™’ †’ Š¡¦`=‡\’e5‰yˆ” – š‰†‰ X‰[Š[Œ Remark: Show this anlytically. Ž/eAct020010distance06-6.EAC0100000029a1É distance06-6.EAC† main.ACT† †#†-ˆ0†4ІG^E ˆŒ'[†4ˆ7 Example 1ˆs Œ!'Consider C1:y=x^2+1 and C2: y=-†-1. †G†ª5For every point on†9 , we can fi†9the correspondingŽk?”22 so†(atŠ-ÿ isŠ= shortest from†˜ to C2.\Œ²†©†™Œª ©Έú‰Î7‘ ‹< (0˜Ye† `YdG€D Š Š'‰‘@v"p‰›˜Dvq‹{r† †A† † †L† †Œ C˜ u˜x˜yŽ †R† †Å@! ŽNŠDHŠC@†}Ð6–°†„eqhC…† ™2I†š˜††°ÈÈ ŽU–B (F††c†Ð Y™qA†6dŠ q–QqІ3†ò1Æ¢—‡ÉÀ–­íëx^2+1† H–%‡15Ä@† †ÄÈ #ŠèA˜Ö‰[LY™ˆCŠ`’Ž  ‡†ʘ~ -Œ-1šC–O† ™2e0b† —† †!Ä@  $ †-ÈÈ"Ž@†<Ð6–°†CqA†6d†HY™ (F††cŒT‘2R–‚Š`†k W–2g”‰fŠ@ †€Ře ††††ž.ɘ†ƒ3ÈÀ– Ž4ˆ¢0ˆˆ4†8.ÈH!œhˆˆdˆ<ˆ"ˆ@ˆˆ†š1¢šˆPH–vžƒˆ·†Y2ˆ!“f[‹u)(step1: construct two curves, C1 and C2. Ž0 step3: fix the curve C1. -ˆ 2: construct a tangent to† Œ1 at C2. Œ6LŽV˜6perpendicular lineˆAˆtPІJ a given point‰NˆS4: sele††ˆ¬inters† ion betweenŠÅnormalŒdand†Ï (**sometimes we Ž©can†/t‡nd‡ is using CP)zQˆz 5: animateŠbŠ› (which†O•eˆFœÓ) along‘[—'I%step6: collect point C on C1) and theŽAŠ2 afterŠanimation. .ˆQ7”QonlyŠC x-values for†aˆZA. Œ5 Ž?7T†nfirstˆ“umn=x Š8Œ’ (wˆ †S concentratˆŽH/”¬that isˆÉlow†¯half ofŠÏcircle’´&ˆuseco†îŽv –w‰ C2. 2Œç -0.5662567048Œ†1– 374790992Œ†3 09591836735–H0870149Œ)Œ'469”q 480666535Žq-0.08775510204 † 4541168738ŒŠ) 367346939–) 282170287–)79591Š.–R 030598316–Ry0Žgˆ{37†h6789Ž=Š{71†i5†–R 354416394ŽŠ¤Ž¢87˜R 307444935–Í 6326530612”¤3075†ä471–ÍË4Žâ‰ 284700324˜R’Ì–R 262606549˜¤ô‘ ‰q240512‡ŠŽ=‹qŒÊ‰ž•š 218419000‰H-0.0428571†6† † 1970678738” 0387755102–(7†;67471ŒŠQ3469Œ,–Q54736944–= 0306122449–y 336643104–Q265Ž+–)13055831޶ŠËˆM89795ŽRŠ 920760287˜S18367ˆ©˜h7156†æ0‘ ŠÎ‰‹ ˜T 509519019 Ї0408163™ 0‡\‡!0 -6.Šõ898îìë˜, 101062681ŽV-2‡ŸŠR27–- $0.010223717742.040816327îìë3Œ †+ 3046087267Œ+ 6.12244898ž* 5097652055”†iŽY”R 714921684Ž}ˆf 1428571429Œ †¥†%93478– 183673469Ž;†' 1127091262”´Œ 795ŽN 0.1336889`ˆÚ265306ˆÍ’t 1545759008”‡Ž$4”š 175555703‹'4693877ý†Á1969068‡A”ÔŒ#‡’À 2186292811”À‘ 86“240258Œš 0.04693877551ˆ 0.2623526†Œˆ' 5102040816”'84724943Ž:ˆN†GŒ(2’N 307561365Ž:ˆu 5918367347’u 330304957Ž:ˆœ 632653061–N54255351–œˆIŠÆ8’à 3782057459”Ã714285†3’œ40289878¯ˆÃ‰ Œì“ 428055985Ž:ˆÃ79Å’œ 4539558304”ÃŒç‡dމ‡84†M05492˜'‹‚‰c’œ 508076295—‘76†× 0.5364825769ˆ 0.09591836735Œˆ'65724337Ž0.1\Œ2Ôˆ† ÊŒœN&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°f† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– yEH Š}Y™x’$As†Ø ™˜„hE@e†ñ —@êY†¨4œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈHerC7P‡ ˆR$ˆˆ † ’ ’¢š”<– àHàxਚ2Œ¸†ø‡{†ç$o<†H†T†`†l†x†„††œ†¨†´†À†̇«؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆ@†Lf%g€Y™7G™ Ž p“PŒ€fe5Ž$ThsŽ0(!p(pŒ<˜1`ŒHx6g‰0Œ0TAc”Œ`0tDTSgGŒx„p$Žlb`eIŽ0@Q'uŽtAŽ`—x„uq’HTsiDŽÀ3fC@ŒØXœ v‡Œ˜`8Œ´˜ Q˜tpŒü˜&Œl˜#qwŠ< ˜`‡&Šü †<vRŠ0†’„†ÔJ !“Gƒ‰[†0p‘&Šœ ™3h‰)Œ™TWYŠÌ†uUW‹P†$–h0ŠÀ ™b’Šä ™@%‰Š0  ™b5&uPˆ „rICŒ Ve`Œ00IW Œ$T%SQŽ0x WEŒ<‰‡ˆŽ$(Y…0ŒTS•X0@Œ`€PT’Ž b•ŽT6H%vŽHerC7Ž2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†qü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†Aø(4@LˆÈ‰f Y™ Y6s‹tY˜ † F‹DY˜wU ‹,ˆ 6sF“Ž•‘ƒg‹P†&ˆ#€Œ<(W0‡~Y˜†&‡€‡:2e0a ‡~†/4p‡~Q @`Œ<i8†]ŒH9†S(އuQˆ_†`†_uPŒl$Iކk"@Œ„$H—•Œ†wi†5$B…qB†ƒ´$H˜ŒH—†š2Œ¨–  —”$ˆ < –T† ’l†„† œ†´†̆ä† ü — —, —D —\ —t —Œ ˜‘¤ˆ#U‡u•‡™0 ˜6sF“† ˆ wU @Œ†q†Ž Y† PŒ$†©6†9ˆ<™’ 2ˆ †$ ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†4ü†† †,†8†D†P†\†h†t†€†Œ†0†¬@¤† °†¼†ȆÔ†à†ì†*ø(4@Lf%g€‡# Y™7G™ Ž p“‹ Y™€fe5Ž$ThsŽ0(!p(pŒ<˜1`ŒHx6g‰0Œ0TAc”‹xY™0tDTSgGŒx„p$Žlb`eIŽ0@Q'u† Y™A`ˆ — xs€Ž uq†8ŽTsiD †}_3fC@Ž0X1Ž< v‡Œ˜`8ŒT˜ QŒT˜tpPŠ<˜&Œl˜#qwŠ< ˜`‡&pŒ  vRŠ0 ˜’„†ß !“Gƒˆ³†0p‘&Šœ ™3h‰)†g™TWYŠÌ†uUW†p+™–h0ŠÀ †üb’Šä ™@%‰0b5&uЍ ™„rIC‡; VeŠð ‡0IWŽx‡*%SQ‡Mx WEŒ‰‡ˆŽœ‡^@Y…0Œ¨S•X„€PT’Žb•ŽÌ6H%vŽHerC7Ž2†  $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†qü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†hø(4@L†¼† Y™ Y6sPˆY˜ † FŒ wU @Œ6sF“Ž•‘ƒg0Œ0ˆ#€Œ<(Wކ ‡†!P2e0a Œ`†;4pŒlQ†j`Œ„i8†zŒ†S(އuQЏY˜F“‡uŽ´$Iކk"†&$H—•ŽÌƒg4iŽÌB…qB Y˜0Œ †5H˜ˆY—ˆ2p– Š  —”$ˆ< ˜Œ7Ž ˆGˆÔŒX~e0a"ކmIŒH˜F“‡uPŒH‡uQŒ`˜(W(`Œ`i8wUŒl @ŽQ†Á Œ„‘†yŠ´ ˜2†mŽs†a€Œ¨†UŽ´U†I•†=ŽÌ6†1ŽÌ†v †H †Žä Y† Ž´‰K™’ †”й¦`$= —’e5‰yˆ” – š†ˆ Xˆ\Šlook at x near 0.Ôˆ1†%ʆ4ˆ-\N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°b† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– D€6ŒxG $ˆÑ†0–„rF†ñ —”<Y†¤5 ™˜0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œšx®Æ$ÈH •a(@‡% ™ˆˆ  ™’ ’¢š’ ”HàGàwে2Œ¸†¼‡}†é$q<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆ@† LR#c6PY™– – ®Þ0 ` •8 ‘`Œx yFppŒ$ R‚ g‘q€Žœr0F ލ“„Ž WFgxŽH‡„59ŒÌe@ŽØ0cŽB0U@ŒðHTb…Ž„IRFbŽ`Sp`ŽlQ(V‰Y˜‘‡Š¨ ˜R'hƒŠH †<“0Œ I…sŠT ™ADTŠ„†„ ‰–Š„ ™%DŽ$‡‘rŠl† ÌSIŽ<‡PR†prdS4Ž< tŠ ™ Rxt€‡ˆ yEu6†æ•a(@‘Ä`2†›† ‡«‡¯$†0‡»<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†`ø(4@L‰c‰g Y™yY6pŽ † sPŽ8wU Ž$6sFŒ0—•‘ƒŽ0ˆ#‹ Y™W(W†=†%“Ž 2e0`Œ†-g0Œ$uQŽ0†N-@€Œ<4i8w0†SŽ0“‡uQˆ_†`†_‡Ž0S$PŒx†;ka Œ„$H˜Ž0 †‘Œ˜”T˜†wŒœ˜†GIŒ`˜Œx–  –$†<†T ˜”lˆ„† œ† ’´†’̆$’ä†"ü — —, —D —\ — t —Œ ™W‘¤ˆPwˆIŒœ—‡™p ™6sF† ˆ 8wU Ž Y†PŽy† pŒ$†6†9Š ’ 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LR#c6‹Y™– – ®Þ0 ` •8 ‘`Œx yFp‹xY™ R‚ g‘q€ Y™r0F Š “„Ž WFgx`Œ‡„59Œ$Ce@PŒ00cŽB0U@ŒHHTb…Ž<RFbŽ`Sp`ŽlQ(Vˆw Y˜‘‡pˆ ' ˜R'hƒŠH †<“0Œ I…sŠT ™ADTŠ„†„ ‰–Š„ ™%DŽ$‡‘rŠl†\ÌSIŽ<‡PRŽ`rdS4Ž< t Rxt€Œ„ yEu6 •a(Žœ– ®Þ0Î`2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†yð†vü ,8DP\ht€Œ˜¤°¼ÈÔàìø(4@L†Ì Y™yY6pŽ † sPŽ8wU ‡:"6sFŒ0—•‘ƒŽ0ˆ#@ŒHW(WŒT†!“02e0`Œl†;g0ŒxuQ†2 †j@€Œ4i8w0†SŽ0“‡uQŽ´sF“‡ˆ S$Ž´†kaˆ $H˜Žä ”À˜ŠT Y˜ @`Œ †/*Iˆ†0– Š  –$ –< ˜(WŽ$ 6sFŒ†pˆPŒ0™2e0a Ž S†IPŽˆ€Ž$ˆ‘ Œ`™”T™Š­1Ѝ ™U†µŽ0uQŒ`•‘ƒgŽ0†mŽ0†“Œ™W†©ˆZwˆIŒœ—†=pŒ¨”À™8ˆ%ŒÀY†ÙŽ´y† Ž0‰K™’ †’ Š¡¦`=‡\’e5‰yˆ” – š‰†‰ X‰[Š Ž Remark: Show this anlytically. Œ/eAct020013distance06-atcm.EAC010000005801É distance06-atcm.EAC† main.ACT†#†&†0ˆ3†7ІJ^E ˆŒ'#[†4ˆ7 Example 1ˆv Œ-Consider C1: y=sin(x)+5 and C2ˆ -cos(x-1). †M†³5For every point on†? , we can fi†<the correspondingŽq?”22 so†(atŠ-‘ isŠ= shortest from†ž to C2.\Œ¸"įΉ‰'ÎC‘,‹H…fqƒ † `3€(‰`†`Œ††# †˜Dv‡¼†r† Ž A† † †L† †&Œ C˜ u˜x˜yŽ †_† †!ÄH  ŽNŠÈÀ@†‰Ð6–°†5™Y7†› ™ q•BU‡™Š H˜!U†.`†·†¼ÊÀ!¤BŒ6˜†6Y™ŒNˆ` ™qIs‡BŠB W–2g”‰f€ŽþÅ@–£†µÄÈ еB–¤Q‰‡4ŠŒ—uC5† Ž:ŽAŒ¤ˆ¨†K5Ä ] ‡•‡Œ sin(íëx)+5‹—Š`£Ž ˆ­Ž SEV– —† † .È@ ˆ† †3ÊÀ#” ††† ¢0ˆˆ4 Œ"”ˆ4ˆˆdˆ<ˆ"ˆ@ˆˆ†…1ŘLˆ2ˆPHŽ †§!Ę"†fÈÈf@†ÈÐ6–°†Ï1c”ƒ(ˆÚ™ R% d1‚ˆæ™Gvfi–6† Y™†3ŒBT˜B”6Y™˜NwV‡s†. `W–2g”‰fŠ~†ÅšÅ†µÄÈ"‰eA–¤Q‰‡4ŠJ G tŒ¤<ŽCˆ¤ˆ¨‡§5Ç@!”]†ÊÀ! † † -cos(íëx-1)`– €–SEV–ˆ? —††U.È@ ”Q†g3ËÀ!’ˆu††Š0H–ˆˆ4¢Jˆ4ˆˆdˆ<ˆ"ˆ@ˆˆ†Ñ1Å@"”jˆ2ˆPH–  †÷Ž ˜‹†††Pˆ)† ‘ R‡7‡=#define g(x)=-(x+0.45)^2-0.975RŽ)done[Œ5˜A solve(x^2+(y‡q^2=1,y)Š:Œfy=-Ž -xŒ}2 +1Š +1,y=Ž-xŒ2Œ"†, 1Rˆ=Ž:define f(x)=1-ŽP 1-x^2RŒ'doneŠ8Œ diff(g†5,x)Š(Ž|-Œz20î’x+9ŒR10˜w Žwg1ˆxÈ<²‹&solve((†Žc)-ˆÈ )/(c-x))*†^c)+1=0,cŒ¥2800† c‘'3J +10†–23 -4Š4x-cî’ŽHŒHË{-24660‰´-3600î’†-xŒ 2Ž+1Œ +7839=0[Œ+RŠ1– ŒC\ŒKЈ† ÊŠ2 N&L%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡Ìxy†^‰Ø<†U†y2‡ †³8†i†ä†€L´ä<‰TŠÈäŽP †W †ä† † ‡np’Š©†Ý’†Þ;’”’’ ’’¬’’¸’’Ä’’Ð’’Ü’’è’†ô†ðŠùŒ ‘ †!‘ˆ¾†"‘,$†#‘@0’ˆ‹W<†%‘hH† &‘|T† '‘`† !(‘¤l¸†ä)†x†  †*†y„†}+††,†œ†-†¨†.†´††pÀ†1†̆2†؆3†ä†4†ð†5†ü†ÉEð†F†Ê† H‘ † I‘,ˆú†ÓJ†Ê8†K‘TD† L†ÊP† M†Ê\† N†Êh† O†Ê t’ˆF†Ë€††Æ†Ú Q††Œ†R†ƒ˜†S†¤†‰°†]‡h ¼†i ˆ^ŽÐ_†Ć‰,ȆaŽàb†І”†Ô’Œ•†à† ͆ì†Άø’ˆZ‹ ’ב,† Ø‘@† Ù‘T(† Ú‘h4† )Û‘|@‘ Financial‡ª Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡X‰c ††† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è†]–|œš"˜| “i™” ™‰G‰K† &“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´ˆ²††°† Š” †#’$†(œ†AŠ +†V! 3x(-(-4*x+4*(-x^2+1)^(1/2)-7Ž )/†/2’O(Œ<Š<º:Ž9†›Ž;`– PÎÆ$´$“– –0” – •%i™`‡e —‰@`Y†Û# ™˜<™€(1…0qy`‰X#Y‡uYƒ‡­ ˜–‰»‰ ‡ƒ;Ž ˆ – ˜Æ$ÊH’ ’¤È%°´þaþ þߞجð`@» —’e5‰y`” – œ†ˆ$†Xˆ \ŠΈ† Έ† Š/Š™™™™™™†`V%Œ6† Œ˜† –˜DvŒd†K†r†  A† ŽkLŒ‹ŠxC˜ u˜x˜yŒ¿†qˆq†äˆ@  Œ -íëx^2+-1††ˆ!Œ@‡Ð6–°† Š÷4ŒÖ– ׈GˆjˆˆŒâ[O[Z)(step1: construct two curves, C1 and C2. Ž0 step3: fix the curve C1. -ˆ 2: construct a tangent to† Œ1 at C2. Œ6LŽV˜6perpendicular lineˆAˆtPІJ a given point‰NˆS4: sele††ˆ¬inters† ion betweenŠÅnormalŒdand†Ï (**sometimes we Ž©can†/t‡nd‡ is using CP)zQˆz 5: animateŠbŠ› (which†O•eˆFœÓ) along‘[‹'(J&step6: collect point C Ion C1) and theŽA ˆ2 afterŠanimation. .ˆQ7”QonlyŠB x-values for†aˆYA. Œ6Ž>7T†lfirstˆ’umn=x Š7Šy1 (wˆ †R concentratˆ ŽH/”¬that isˆ²low†¯half ofŠÏcircle´&ˆvseco†íŽw –x‰C2–¬2Œð -0.7526798709Œ†25´ ˆ4 2397959184´Hˆ\22Š&367®p -0.2193877551†Š 8324367047”20918†35”( 745403719–1989795†-”P 680830956–<18Œv02”x6256758†}”Œ 1785714286” 576195262–´16Šž469”È53064†64”Ü 158163265–d 488014869–d14ŒÆ3— 447671078Ž †d13¢Ç4‡+62†;—S12Œí0–‹ 372157965˜Ÿ1ŠÄ38—?33640429“?-0.1071428571 † 3016986366Œ†( 0969387755–) 2678748608–)86734ˆ-Ž †f 234792892–( 7653061224”z 2023324919–)6632Œ,”£170†Ž6503–)5ŠN489ŽzˆÌ138†Ê818Ž=ŠÌ 4591836735”{‡ 674392˜{3‡™޹7393579˜|2‡0204‘ ‰Hˆh82957ŽâŠ)1öŽ|325995ŽS-5‡šŠO16îìëŽç ŠA28260†W5.102040817îìë3ˆ 0.04593284732” 1530612245Œ †( 766890038”'255ŽV’'1†(236359”' 357142857Žb†N1388125†bš‰183673”u 1703357756”°5Š™489Žu 0.20227979–M66326ŠÆ’t23†å9217–M7Œ$22”é 2678199907”'8†–46938”é3016423†”'9ˆ#†®5”u3‡ 46385r#”› 372098048”®11’s 0.4090998654 127551020” 4476058565Œ 0.137Œ'’8 4879460267”K47959183” 5305682809”q 581632653’„5761†971”&68367346”962558†J—†9 1785714286’˜6807†u7–_188 ¾745†•16–ö19†ŠÀ’¾ 832236188”˜20ˆá673”…¨&193ŒtºL2/—C¢r0.2397959184 0.8322361881Œ†&5\Œåˆ† åŒ LN SpreadsheetSІˆÈ †ä†† 2@ˆ † 2@†Rg˜p†DY™¯á´´Ò62Cgp¬lE@7Pª‡€ƒ V®%gX$0ª½vRbªØ0d†‡¦óˆHi`«Ggx¬½ !ƒ¬lrye”l@6@B–PY™¯áši†6`ªg‡H`€ª64y(’ˆP¤Q3$‘ªlp8vP0ª‡8†8ª¢gC’¬Qg95yŒQ˜žØY‚•tŒ¢ S2Y•¬6R‚`•pˆ ¤Q2„s ªf‰8‰^¤6b65н ¡z8%"@¬p3Wu` ™¯á@'—”ˆ¦4s’®6g™pªQd#†®64c…0ª‡r €Hª¢ ˜e@ª½G`XVPªØ‡”`&¬¢0V‚€«vX—¬‡%X€–¬l€su¬ØE(`¬½2#aˆ¬ó¬2#aˆ ™¯á@´¬2˜9PˆPˆY T9yY@¬)Y6p¬68wUŠo¤Q 6sŠp¢l˜—•‘€ª‡ˆ†P ª¢xW(`ª½h6sFªØX2e0ªóG•‘ƒ¬Ø7uQ‡„©)'U ­)4i8ˆØY™¯á@(W¤ i8wUŒ˜ž6g4i8€ªe0a"@ª6c&S¬Qa"D‰¬QY6sPª‡W’½ ¢U @¬¢S$¬Q†5`Š—¨pˆ  ”Q ¡)”‡¢н ª6”ó Q"a"D‰€ ˜¯á@c&Sªe0a"Pª6g4i8¬Q i8wU¬Q(WŒ™ž‡’Q¢'U @¬67uQ†ÄªQG•‘ƒp¬lX2e0¬‡h6sF¬¢xW(`¬½ˆ†ò ¬Ø˜—•‘¬Ø 6s_¡“D‹)@)Y6p ™¯á˜9yY@¬Pˆ2”62ކXˆR!7c† `7 ˆ %>Y™”  ™†“kˆ'a” –Š—[ˆ¹\Œ(6Look at when x near 0.5, we get c about†10 somethingÔˆFˆsÊŠˆ£DN&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°h† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡–  ˜9“˜†Ì Y™ ˜p4w8†Ø ™–„”x@…$†ñ —’Y†ª4œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH2#aˆ‡ * ™PˆŒ ž¢;– àHàxਚ2Œ¸†¼‡†ë$s<†H†T†`†l†x†„††œ†¨†´†À‡«̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆa@† LRg˜pY™– – œ2CgpŽ0E@7PŒ<€ƒ V %gX$0ŒTvRbŒ`0d†@ŒlˆHi`ŒxGgxŽT !ƒ†Crye†K86@B–Žli†6Ž<g‡H`€ŒÀ4y(’ˆË†Ì3$‘ŽØp8vPŽ8†8ˆXgC’üg95yŒ´˜Y‚•tŒH˜S2Y•Œ<˜R‚`•Šü †$2„s Œ f‰8‰C†b65ŠT ™8%"ŠÀ† p3WuŠ´†'—”Œ0™4s’g™‹†-"d#† 64c…ŠÀ ‡ €H‰P ™ ˜e@‡4ˆ YG`XVPŽ ‡”`&pŒ0V‚€Œ$vX—Œ0%X€–Ž0€su0ŒHE(`ŽT2#aˆŽ0– ®œ2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†oø(4@L‹XˆØY™9yY‹ † )Y6‹h†8wUŠü†$ 6s‹\Y™˜—•‘€Œ<ˆ†# ŒHxW(`Y™h6sF‡a'X2e0ŽG•‘ƒpŽ$7uQˆ/ˆ0'U @Ž<4i8€Ž‡_ (WŒT i†l!Œ ˜g’$˜e0a"Œ<˜c&SŒ0˜a"D‰DŒH˜Y6sPŠœ˜†§ŽT˜ˆwŒl˜S$Ž$†ŽŒÌ—Š Š´ —”$ –< ŒT Œ”l†„†œ Œ´ŽH”Ì ˜”äˆ8ü —† “,†“D†$“\†0“t†<“Œ†Hx‘¤†Tˆ†kŒ´™˜—•‘€ ™ ˆ† ˆ 8wUŽ )†¢#pŽ9yY@Ž$Š,Œ0 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†Uø(4@LRg˜p‡#Y™– – œ2Cg‹0†0E@7‹TY™€ƒ V %gX$0ŒTvRb‹lY™0d†‹`Y™ˆHi`ŒxGgxŽT !ƒŽ0rye‡ Y™6@B–PŠ i†6`Œ g‡H`€Œ4y(’ˆ#†03$‘Œ0p8vP0Œ<8†8ŒHgC’Ž$[g95yŒ$˜Y‚•tŒH˜S2Y•Œ<˜R‚`•pˆ  †$2„s Œ f‰8ˆ›†b65ŠT ™8%"@Ž p3WuŠ´ ™'—”†w™4s’g™Œ`™d#† 64c…ŠÀ†*r €HŠ  ˜eŽ`†ö`XV‹ †F‡”`&Œ¨‡V‚€ŽvX—Ž<%X€P†h€su†43E(`Ž´2#aˆŽl– ®œ2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†ð†wü ,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LP† Y™9yY@Ž )Y6pŽ8wUŽ$ 6sŠ4Y™˜—•‘€Œ<ˆ†# ŒHxW(`ŒTh6sFŒ`X2e0ŒlG•‘ƒŽ`7uQŽ„'U ˆB4i8`(WŽ„ i’˜g’$˜e0a"ŒÀ˜c&SŒ´˜a"D‰Œ¨˜Y’À˜†§W ˆ´Y˜U @€Œ S$PŒ†`Š —†pˆ  —”$ –< ˜†© W ŒY6sŽ$Š[Ž$ŠlŒ<Š~ŽHg†¡† i‡Ž$†TŒ ™’$†'ˆyŽˆÕˆËˆ$ˆæŒ¨™ŒøŽ<‹ ŽH"x†©ŠØ†Tˆ†kŒ´™˜—•‘Ž` ’À™’†J)†Ù™9yYŽ„‹4Œ¨ ˆŠõ¦`‹d\’e5‰yˆ” – š†ˆ Xˆˆ[Š Remark: Show this anlytically. Ž' ˆK Example 2.\ŒA (x+2)^2+(y-ˆ=4Έu!†gΈn† ŠˆŠp(Xh†† `s‘hƒ@†`%ˆ‡†Sˆ0†йDvŽÂˆr† Ž A† ŽkLŽ'‰C˜ u˜x˜yŽ ‡-ˆq"‡=5ÄH! ‘7#‡OÆÈ  D@†Ð6–°† “‡uQ† ™uˆPG†$`†(†ŠŠ$†9ÈÀ   -íëx^2+-2ŒCŠCˆIŒ<Y™˜D2f† ˜†%†ˆ2À@–O&†š@HŠaEš¤PUA†¼Y–I†Ç ¤'†ÝAHŽCF˜ç •&E‰D†ÿ Y•˜P9¨C(‡ Ř˜ˆU)‡6ˈ# Š—?’;`” – Šd*ªX+‡U•U–° 26‘tp#‹HaPuhGH‹£ 6‘q ™†'† ,† Å@  † †&†)†-†'Ä +–".†I!ÇH–"/†[ÈÀ@†jÐ6–°†qaPuhGHŠ| 26‘tp#Šˆ‚––QC†.†˜ +W–2g”‰fŠ@0¢¡ˆ8ˆ‡ˆ‹1†q.Ș2†3”ƒ†$Ž4ˆ3¢0ˆˆ44¢Jˆ4ˆˆdˆ<ˆ"ˆ@ˆˆ5‡!1Ä@!œ2ˆPˆæ6‡fÊÀ– -íëx^2+-ˆA•Ž ˆ0¦ˆÚ‰a‰i‰¥ŠØ"††† [2† -3.044445151Œ-0.5 2.887509543Œ † 4897959184”'76420461ŽŠ'Œ%367”N6585292šN6938775€ˆN5†N1653Ž:Š'ŽL3–œ47801798˜œ’”Ã3†¯82899–'Žs02”ê 322826416–'28571428ŽˆÃ25164573˜'Šæ346Žb‰8183†b61˜u08163265ް‰_11870707—8ˆ¯‰^þ -2.056039352 -0.38775510’ 1.995448424Œ ˆ&Ž%0ŽŠ'3666736Ž:Š'†469388”N 879471899–'571428†”u8236707›ŠuŠKˆŸ”œ 769098183–'vŽbˆÃ71†ê9076–'26530612–ê66307†ìŽaŠ'16Ž*”N61137841’¯†'ŠJ44–t‡\415šÂ295918‰Œ †M‡l090‘I‰]‹ ‹”M4‡©1179Žû -0.2755102041 -1.41099718Ž ˆ' 653061224”' 362067023–'ŽM08”N 313445597–N 448979592”N†b05986ŽaŠ' 346938775”N216838†+–'’O”N†&71153˜N14285714ްˆê1206093aŠ'ˆ¾1632ް‰0724616”¯0.1Œ™5$ †M0241976ކ‰618367ˆÅ–Õ97574443š(Š%†ê7ˆÖ92‡[6‡<—_ˆ—‰­ -0.8779634832 † 1530612245” 8284726494–(42857†9”< 778463228–<1326ŒS”P72783725šx†s489†‘”P 6764867528Œ †´1Ž)Žˆ; 624291512–³ 1020408163”O†¯11451Ÿ‡ 0918367346–È 516798247˜)ˆLŒË•-46115†¦37–)‰‹–{ 403965459˜)‹gŠô•W34‡f4698ŽŠ)5’Ψ-0.2837326024†040816†53Œ ˆ) 198329558” 0306122449”( 152505707˜Q2’S– 804638348ŽfŠ1’,Œ-9.950126459îìë5Œ¨0\Œ± scatter plotÔˆÅ7†ÉʈÏ|N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– 4ˆyqYtŒx3Pcp‰†Ù ™–„!—’G †ñ —’éY–$œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH •&E‡ %Y•ˆˆ Žœ¸†’ – øTøÊÌ2Œ¸†¼‡v†â$j<†H†T†`†l†x†„††œ†¨†´†À†̆؇ªä †ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆx@†LDE`ˆu T0Ž vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A`ŽT%Es 7ua$‡``95 Œ„™THBŽx“fg6‡”q†L‚6pu0v˜Ž´qV Žxf0tHPŒØaxAŽäV’<Qˆû†üFy0A —6 gˆ14EYކ)&PY† !h8Pl‡S8 7„$aiäA—i†’ utD6‹8Y™ 'a4‹€† w–4ƒ‹†(G&I‹Œ†xF2(ˆØ Y™'ƒrS ‡- † vHgR€‡-$)PŒAqE y‚GŽagcpŒ<–TYŽ D”F˜ŒTƒs&@Œ`ƒ)UŽ`RPW†3"cƒH0Š„˜ •&EŒ<•2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†aø(4@L‰c‰g‡t‰yY† 6‘Di8wUŒY6s€H—•‘˜ˆ#°(W(`Y™†"FŽ 2e0Œ†+ƒpŒ$‡uQˆ/†0†N @Œ<g4i8€ŒH†SW‡yF“‡uPŒ`†_“Ž`&S ŒxˆkŽ„$IŽ`†wg†…qB…Ž„† ƒŽ`e0a"ˆˆ†.D‰yYŠ.›w†>"$H—•Žä(WŽäˆñŽä†³QŽäƒ†Ùˆs†Íˆc†ÁŠË$ˆ B†©D‡Baˆ "†‘h$H˜ˆ4ˆyh •€˜‹˜˜”¨˜†Á¤˜‡~` Y˜2e0† † ŒÍ)†ˆˆ`Œˆ Ž$ŠŠ$’ ” 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†$ø(4@LDE‡ #`ˆu T‹$† -vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A‹T†:.%Es 7ua$‡``95 Œ„™THBŽx“fg6† †lT‡”q‰Š ‚6pu Ž v˜0ŽqV `Ž$f0tHPŽ0axAŽ<V’<QˆSˆ`Fy0A —06 g†s014EYpŽ„&PY†@Ž!h8Pl‡S 7„$ai´A—i†– utD6ŠØY™ 'a4ŠÌ† w–4ƒŠä†(G&IŠl†xF2(Š('ƒrSŽ$vHgR€ŒH$)†²qEŽ0y‚GŽ<agcŠÌY™–TŒˆd D”F˜Žƒs&‡Aƒ)UŽ`RPWŽcƒH‹€Y˜ •&E‹¤Y•2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†_ø(4@L† Y™‰yY@Ž † 6pŽi8wUŽ$Y6sPŽ0H—•‘€Ž<ˆ# ŽH(W(`ŽT†FŽ`2e0Œl†;ƒ†‡uQŽ„† j Ž„g4i8Ž`†SWˆF“‡uˆ6sF“†@&Sˆ0ˆkˆ.$IŽä•‘ƒgŽ„…qB…p ˆ®Y™†Z Ž e0a"@†ªU @€†ªD†Â †ª†jwPŽ<$†³†¬†­0†¬†¥pŒ`†{Qˆk†lƒ†—†¾s††Æc†‡Ž„AS$Ž`B…qBŽ`2†Ž„"†‘`ŒÀ$H˜`ˆyŽ„ 6sFŒœ˜†Že0Œ0˜”¨†djH—ŒÀ˜†ïŒT˜ˆ¿eŒÌ˜†IŒÀ˜ŠØŒx˜–lŒ‰O Ž ’ ‹a¦`ŠÈ‰Œ —’e5‰yˆ” – š†ˆ Xˆ†[Š Ž Example: Another eŒ Œ)\Œ1 animationΈ8†ÎˆVŽ\ŠwVYrq’† `9ef‰•Š ’G5‘'† @ˆ™Š ŽDˆ³v’K†r† Ž A† 'LŽ'ˆçC˜ u˜x˜yŽ ‡9†Æ@  † †:†ÁH"ƒŠG@†&Ð6–°†-D‰X’BE†& 4u„g€†Š <Ž ;†Y ÈÀU–B%‰‚ƒ†z ™ t'pˆ` Y™•xaF23Š †3<†BÈÈ ƒ`Š…E˜…Ph¶†Ož…=†ÞÉÈ ŒCF˜È”7˜ùŒz˜C>‡!Ä™ˆ˜ˆÞ?‡;ÅH–ˆoˆñÇ¡UA†‘ÉÈ!¥@"p„‹ h!G !R‹"77#5ˆ¢‹dˆFBŽ”†F†C†ÈÈ ƒ`ˆC@†Ð6–°†€Ž%` Ž  ™’ ŒD†C ÈÀ! Š–B)€XB†6 Y™vuWHq•Š 4V3Q1І3=މE†•Ä@ ŽJŽˆ`B†1Ž"ˆ?†>†;Ž$FŠ:H–:<†GŠšÈ–Ü h€†0ŠÐ)#IX–ŠÜ&ifH49Šô†H"D™ˆŠYP” Ÿˆ‰I¢ŸˆYˆŸF Ž"ˆˆ.J¢Íˆ.K‡² ËÈ#gÐ6–°†R2—X€b† Y™ 5‡Y!‚‘† ™Gd‰T˜†*`†.C† H†L†;ÄH  † †ŒK†QJÿÿÿÿŽ"ˆˆ.ˆM†m5Å@!’2N†DÄÈ ŠDA@”Šn†&6†¨ƒ?†½O†ÂÊÀ!”‡-(íëx+-1)^2+-4˜H«ˆ×PC yHqyHr‡  ˆèˆÇ@–ÛQ‡(ÃH©B¤©–©ˆ ¢©A†RŠYH–­ˆYS†ÃÊÈ‘—h!G !ˆª ™@"p„‹” V ”t…†Q† T† !Ä@  † †S†AW–2g”‰f€†U†4Ř'N†A††V†R.È@ ’W†d3ÉÀ!”OŽ4ˆ_X†‚.ËH–0ˆˆ4Y†œ.ʘˆ4ˆˆdˆ<ˆ"ˆ@ˆˆZ†š1¢šˆPH–vžƒˆ·‰CŽ)K†<†G†=†;†D†:(ˆAM‘$ [(‡L -0.5229403823Œ0.8” 3946122586Œ 0.8179487†”E 264952635Ž;ˆ'† 97435ˆ' -0.1338658196† 0.8538461†Œ-1.252210698îìë3”+71794†Ž+†> 1329899095”Q 897435897’d 268966744”& 907692307”&4067†ž94”9 925641025ް 0.546562241’Â9Œn43”Õ688409†˜4’„9Šäˆê”û 324496012’ã9Œá7–Ð978805‡•49âŽ_ 1.1276045- 1.0œo†2789807‘iˆ$3333†”643‡006ޏ 1.051282† 1.590014988’ 069230769’$74996129”6 087179487’H 913061434’Z1mŽ2.0†372246’~1Œj23’$24935616”14102564~ 2.42288213”´15897435´2.600†j522’ê1Ši07´ 2.78156478¢1.1ˆÔ†Ú”´96709031”´2CŽ´ 3.156‡!’é1.Ö³ 3.3514836–³2Œj4³3.55‡v341”26666†‘g3.755053048 1.284615385Ž 3.964578506’$ 302564103Ž 4.17957508”H 320512821’$4002871˜H3Žm’H62696877~1.3Šj†p’l85988425Z 1.374358974Ž 5.099308679’Ø 392307692’$34552861Ž$ 1.Œi4Y5.Œj33”k428ŒÙ’k85956060”³4B4³6.‡ 00†¥‘11.4ŽÖ޳ 6‡45209•f4Žj² 6.68945373œ 1.5[\ŽÔˆ[† ÊŠ¨N&à%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H„ ˆ^<̇P_PP†iŠ`dˆZ†faxˆãbŒ\† d †FŽde´ä†”Èh’´•Üt†Íð€†ΑŒ† Б˜† ב ,¤’Ø‘@°† Ù‘T¼† Ú‘hȆ 8Û‘|Ô‘ Financial‡ªForma†¾ †††Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– W&DŠx8–Š$–„B˜9UW†ñ ˜pê ™”`˜0™ (1…0qy`ˆä#Y‡uYƒŠH–˜œšH®Æ$ÈH%"i€‡/Y—qyHqŠ  ™ˆˆŽœ¦’ – àHàxਚ(Œ¸†¼‡~†ê$r<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Oü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDtÔ"”‚0‹ ™”a"X`‹¬™d•&5‡¸ Y™3†X`Š %"i€Š —2˜™ Pˆ ™h–gDŽ xe”pŒFV"Aˆ;†$ˆ@™@Œ02D– Œ< x€QŠ`†7UvSˆk'‰€sŠl† C0pŠ<†Y˜t™a)Ž$‘0aCŽ$”r$Š´$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÌˆ$–p1Ž<i–Ž5ƒcˆ$UcAŽ0uPSލ–ExPŽx•uŽÀ@‡†0ObihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ( † ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ†£0 ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i#†}%d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( QŠx †P#†ˆо $‡”†¹&fffpŽ(F8PŽ$0†¥0Ž02†u<3ŠÑH5ˆ»ŽT7†»@Ž`9†m ŽlAVAˆwˆxB‚†DaS„&<F†%<H Q(<ŠŒŒ´ (†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ"”‚‹DY™”a"X‹,† d•&5Š3†XŽ%"i‹\Y—2˜™ ‹Œ ™h–gDP ™xe”pŒ FV"Aˆ†ˆ@™@Œ$2D– Œ0 x€Q`Œ<vSˆG '‰€s€Ž C0pŠ<†Y˜t™a),Ž$‘0aCŽ$”r$ŠT$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÀˆ$–p1Ž<i–Ž5ƒcˆUcAŽ0uPSލ–ExPŽxg•uŽÀ@‡ŽbihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ(† † ††$†0†<†H†T† `†$lx†)„††œ†¨†´†À†̆؆ä†ð†Nü ,8DP\ht€Œ˜¤°¼ÈÔ† ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i# %d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( Qx#†Ùx$‡”x&]fffx(F8 P0%d0Ž 2‚Ž3„aS€Ž$5d%`Ž07CX—@Ž<9#i ŽHAVAˆSˆTB‚<DaS„<F†%† 6H Q(<ŠŒŒ ˆ®`VŠi†Í ˜’e5‰yˆ” – œ˜`†‰XˆŽ†’[Œ eActfH x1-à(1-x^2)gH$x-(x+0.45)^2-0.975g1H(x((-(20*x+9))/(10))h1H@/x((-à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))h2H@.x((à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))020012eActivity Save.EAC010000005f49É distance06-2a.EAC† main.ACT†!†$ †.ˆ1†5† ІH^I ˆŒ'5[ˆ7 Example 1ˆt Œ'-Consider C1: x^2+(y-1)^2=1 and C2: y=-†-1. †M†±5For every point on†? , we can fi†9the correspondingŽq?”22 so†(atŠ-‘ isŠ= shortest from†ž to C2.\Œ¸8į(†¥-(x+0.45†Ñ -0.975)Ή‰=΋Y“B‹^ (0˜YP† `€„PpB`Š Œ0†  9I)W2†† † v† ††r† Ž A† 'LŽ'Š C˜ u˜x˜yŽ †qˆqˆu9ÈÀ  ŠK5@†ŽÐ6–°†dCfqtŠ ƒ€(g¬ŽGŠ©Length of DA: ÿÿü†ž'ŽzÄÈ ŒqA˜qAw!Q‰ˆ‡ Y™ †q2gFŠ žKœCD˜´—ˆfŠC8#hU‡_ ˜ µV9Ë’û4šû&“”ûvGˆs#q¢ûSlope of tangent at A: ÿÿü††#†&І.††;ÈÈ" Š@†JÐ6–°†QS0RA†\ ™ w7DXyŠ f€ˆVe†.N†F9ÈÀ ŠF3–Gd6a—ˆY ™4—0u˜;˜ªÀDÂÀ ŠÀÀ ¨À—ˆf†y Y™ vcAŠ 8#hU‡4Y˜ŽN œÀ2šÀ”–Ày&c7‰¢À Coord‰€µu‡m†Ž “71@†Ð6–°†Cfqt† SDƒŠ ˆ*ˆ.Ž  Coord of D: ÿÿü†ž%†Ž †n!Ä@  " † †„ÈÀ–Œ vcA†¥ ™—ˆf† Y– ™W–2g”‰fŠ<†ÓŘeˆˆeˆiˆ1šƒˆÚDHŠ•E™  (0˜Wxu‡% Y–fe8(‡†2`˜†‡FÊÀ!”Ø-(íëx+0.45)^2-0.975†H†¢ ‰\‰ ˆ‡‘5Æ@!š¾‡#Ȉ  ¡#†Š’ – 95C†+ ™’1Y– ™&X"xH†O ˜††XÄ@  G †††šˆGˆ†Œ2À˜†ÀH"ŠFB@†®Ð6–°†µ•4VŠ••T“b—9й˜Ñ†œCC˜C&GPŠÌ3G‰ —žCвH–˜ˆUˆÌª‡TÈÈ–µ w7DXy‹>S0RA‹V%1Vgwc‹VŽF¢v‰ˆv‡´Å‹\††Ž†5Ä@  ކ&94x&†1Y™Ž– † ™Q‰‡4r†U ˜†ˆA!šJ†pW–2g”‰f@†!†…Å qˆˆ“"†£.ɘ#†µ3ÈÀ–Ž4ˆ_$¢0ˆˆ4%†8.ÈH!œhˆˆdˆ<ˆ"ˆ@ˆˆˆî1¢šˆPH†–z† ˆ!Žˆ“‘Z–)† † † ††‰Kˆ@‰•Pˆ ‰‹“l\¯Έ'† Άˆ Š ™™™™™˜† `@”Gs Š ˆ.†ŽŠ –DvˆŠK†r† Ž A† ŽkLŽ'ˆxC˜ u˜x˜yŽ †qˆq(†¾.È@ ˆŸˆÊ)†3ÈÀ–*†š-(íëx+0.45)^2-0.975†+‡ ÄH ˆìC@‡Ð6–°†m`ŽÖY™ ƒŠñŠ ˜†,†l”l–Bw‘etd†* ™ „vS€Š !4%8‘G-¢ÒˆÀˆÖ.¢ìˆ±)(†,†.†-†)Ž/†1Å@  † †+†*†HŽ 0†>ÄH–"1†PÈÈ@†_Ð6–°†fhW„p˜‘†q Y™ …h‚6&Š ‚€!‰€†‰Y—†32†TÄ€¦B %a1† –T!G†" † †3†Bʸ4†–†–`†‰B–—ge(Y•Š™—#†XxŠa˜<–ÙˆÝ5Š]˜óˆ]ˆµˆ6Š{H!’7Ž{Š{™Y9ip‡‰ƒ ™‰‡žz8‡£ ÉÈ ¥S ƒ—8E1I ™x1(G’d† YŠ HІ9†!ÈÈ `† @†0Ð6–°†7Œ*†Aˆ6`&GŠ" ˜Š)Š.Š7†:†gÄ@! ˆX8†6mhŽ"ˆˆˆ22†*†Ž ˆˆ94†1†+†,Žsˆ-Ѝ [†â -.3593914697’ 9832099058Ž',ž5 1783128480Ž 0.0160261547R‡<Œ`"define g(x)=-(x+0.45)^2-0.975RŽ)done[Œ•–Asolve(x^2+(y-1†;=1,y)Š:ŽÆy=-ŽÒ -x2Œ+1Œ +1,y=Žª,’5RŠEŒLdefine f(x)=1-Œb 1-x^2RŒ'doneŠ8Œ diff(g†5,x)Š(Ž|-Œz20î’x+9ŒR10[Œ¾*We Žuthˆ rivative of g as g1 below:˜© Ž©g1ˆªÄn¶½g1(c¸¶cÞ¶fˆ¶fš¶ªdefine f1(x)=diff(f† ,x)RdoneRˆ ŒŠ.Š!Œ"xŒ,-xŒ72Œ?+1–=†k0.5Œ`Œb3Ž3ŠgŽX g(c)-ˆ’ŒŠc-xŒ” *g1†+1=0ŠªŽ‚-c+£9Œ–20 ¡-¼¿ŽÜL7M40øî’Œ820î’c+91†Žx-cSŒ¹Ð싟˜ìPî’c+Œ 9Ž20Œ 2Œ%-0-x +1ŽML7M40Œjx-cuî’¼PŒ +1=0[†±Ž§ g(c)-f(x)ŒÁc-xŒË *g1†ˆ5Ê.f1†Eˆc {x,c}[R‹‹# &solve(((’z)/(†v))”q ,c)RY8000î’c‘K3$ +10†–23 -4Š4‡)î’‘¡ŒH2Œ+1Œ-24660Œ -3600î’Ž-x®; +7839=0[Œ[Rˆa– \Œ{Ј;† ÊŒ N&L%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡Ìxy†^‰Ø<†U†y2‡ †³8†i†ä†€L´ä<‰TŠÈäŽP †W †ä† † ‡np’Š©†Ý’†Þ;’”’’ ’’¬’’¸’’Ä’’Ð’’Ü’’è’†ô†ðŠùŒ ‘ †!‘ˆ¾†"‘,$†#‘@0’ˆ‹W<†%‘hH† &‘|T† '‘`† !(‘¤l¸†ä)†x†  †*†y„†}+††,†œ†-†¨†.†´††pÀ†1†̆2†؆3†ä†4†ð†5†ü†ÉEð†F†Ê† H‘ † I‘,ˆú†ÓJ†Ê8†K‘TD† L†ÊP† M†Ê\† N†Êh† O†Ê t’ˆF†Ë€††Æ†Ú Q††Œ†R†ƒ˜†S†¤†‰°†]‡h ¼†i ˆ^ŽÐ_†Ć‰,ȆaŽàb†І”†Ô’Œ•†à† ͆ì†Άø’ˆZ‹ ’ב,† Ø‘@† Ù‘T(† Ú‘h4† )Û‘|@‘ Financial‡ª Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡X‰c ††† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è†]–|œš"˜| “i™” ™‰G‰K† &“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´ˆ²††°† Š” †#’$†(œ†AŠ +†V! 3x(-(-4*x+4*(-x^2+1)^(1/2)-7Ž )/†/2’O(Œ<Š<º:Ž9†›Ž;`– PÎÆ$´$“– –0” – •%i™`‡e —‰@`Y†Û# ™˜<™€(1…0qy`‰X#Y‡uYƒ‡­ ˜–‰»‰ ‡ƒ;Ž ˆ – ˜Æ$ÊH’ ’¤È%°´þaþ þߞجð`@» —’e5‰y`” – œ†ˆ$†Xˆ \ŠΈ<† Έ† Š/Š™™™™™™†`V%Œ6† Œ˜† –˜DvŒd†K†r†  A† ŽkLŒ‹ŠxC˜ u˜x˜yŒ¿†qˆq=†äˆ@  Œ -íëx^2+-1†>†ˆ!Œ@‡Ð6–°† Š÷4ŒÖ– ׈GˆjˆˆŒâ[O[Z)(step1: construct two curves, C1 and C2. Ž0 step3: fix the curve C1. -ˆ 2: construct a tangent to† Œ1 at C2. Œ6LŽV˜6perpendicular lineˆAˆtPІJ a given point‰NˆS4: sele††ˆ¬inters† ion betweenŠÅnormalŒdand†Ï (**sometimes we Ž©can†/t‡nd‡ is using CP)zQˆz 5: animateŠbŠ› (which†O•eˆFœÓ) along‘[‹'(J&step6: collect point C Ion C1) and theŽA ˆ2 afterŠanimation. .ˆQ7”QonlyŠB x-values for†aˆYA. Œ6Ž>7T†lfirstˆ’umn=x Š7Šy1 (wˆ †R concentratˆ ŽH/”¬that isˆ²low†¯half ofŠÏcircle´&ˆvseco†íŽw –x‰C2–¬2Œð -0.7526798709Œ†25´ ˆ4 2397959184´Hˆ\22Š&367®p -0.2193877551†Š 8324367047”20918†35”( 745403719–1989795†-”P 680830956–<18Œv02”x6256758†}”Œ 1785714286” 576195262–´16Šž469”È53064†64”Ü 158163265–d 488014869–d14ŒÆ3— 447671078Ž †d13¢Ç4‡+62†;—S12Œí0–‹ 372157965˜Ÿ1ŠÄ38—?33640429“?-0.1071428571 † 3016986366Œ†( 0969387755–) 2678748608–)86734ˆ-Ž †f 234792892–( 7653061224”z 2023324919–)6632Œ,”£170†Ž6503–)5ŠN489ŽzˆÌ138†Ê818Ž=ŠÌ 4591836735”{‡ 674392˜{3‡™޹7393579˜|2‡0204‘ ‰Hˆh82957ŽâŠ)1öŽ|325995ŽS-5‡šŠO16îìëŽç ŠA28260†W5.102040817îìë3ˆ 0.04593284732” 1530612245Œ †( 766890038”'255ŽV’'1†(236359”' 357142857Žb†N1388125†bš‰183673”u 1703357756”°5Š™489Žu 0.20227979–M66326ŠÆ’t23†å9217–M7Œ$22”é 2678199907”'8†–46938”é3016423†”'9ˆ#†®5”u3‡ 46385r#”› 372098048”®11’s 0.4090998654 127551020” 4476058565Œ 0.137Œ'’8 4879460267”K47959183” 5305682809”q 581632653’„5761†971”&68367346”962558†J—†9 1785714286’˜6807†u7–_188 ¾745†•16–ö19†ŠÀ’¾ 832236188”˜20ˆá673”…¨&193ŒtºL2/—C¢r0.2397959184 0.8322361881Œ†&5\Œåˆ?† åŒ LN SpreadsheetSІˆÈ †ä†† 2@ˆ † 2@†Rg˜p†DY™¯á´´Ò62Cgp¬lE@7Pª‡€ƒ V®%gX$0ª½vRbªØ0d†‡¦óˆHi`«Ggx¬½ !ƒ¬lrye”l@6@B–PY™¯áši†6`ªg‡H`€ª64y(’ˆP¤Q3$‘ªlp8vP0ª‡8†8ª¢gC’¬Qg95yŒQ˜žØY‚•tŒ¢ S2Y•¬6R‚`•pˆ ¤Q2„s ªf‰8‰^¤6b65н ¡z8%"@¬p3Wu` ™¯á@'—”ˆ¦4s’®6g™pªQd#†®64c…0ª‡r €Hª¢ ˜e@ª½G`XVPªØ‡”`&¬¢0V‚€«vX—¬‡%X€–¬l€su¬ØE(`¬½2#aˆ¬ó¬2#aˆ ™¯á@´¬2˜9PˆPˆY T9yY@¬)Y6p¬68wUŠo¤Q 6sŠp¢l˜—•‘€ª‡ˆ†P ª¢xW(`ª½h6sFªØX2e0ªóG•‘ƒ¬Ø7uQ‡„©)'U ­)4i8ˆØY™¯á@(W¤ i8wUŒ˜ž6g4i8€ªe0a"@ª6c&S¬Qa"D‰¬QY6sPª‡W’½ ¢U @¬¢S$¬Q†5`Š—¨pˆ  ”Q ¡)”‡¢н ª6”ó Q"a"D‰€ ˜¯á@c&Sªe0a"Pª6g4i8¬Q i8wU¬Q(WŒ™ž‡’Q¢'U @¬67uQ†ÄªQG•‘ƒp¬lX2e0¬‡h6sF¬¢xW(`¬½ˆ†ò ¬Ø˜—•‘¬Ø 6s_¡“D‹)@)Y6p ™¯á˜9yY@¬Pˆ2”62ކXˆR!7c† `7 ˆ %>Y™”  ™†“kˆ'a” –Š—[ˆ¹\Œ(6Look at when x near 0.5, we get c about†10 somethingÔˆFˆèÊŠˆ£DN&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°h† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡–  ˜9“˜†Ì Y™ ˜p4w8†Ø ™–„”x@…$†ñ —’Y†ª4œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH2#aˆ‡ * ™PˆŒ ž¢;– àHàxਚ2Œ¸†¼‡†ë$s<†H†T†`†l†x†„††œ†¨†´†À‡«̆؆ä† ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆa@† LRg˜pY™– – œ2CgpŽ0E@7PŒ<€ƒ V %gX$0ŒTvRbŒ`0d†@ŒlˆHi`ŒxGgxŽT !ƒ†Crye†K86@B–Žli†6Ž<g‡H`€ŒÀ4y(’ˆË†Ì3$‘ŽØp8vPŽ8†8ˆXgC’üg95yŒ´˜Y‚•tŒH˜S2Y•Œ<˜R‚`•Šü †$2„s Œ f‰8‰C†b65ŠT ™8%"ŠÀ† p3WuŠ´†'—”Œ0™4s’g™‹†-"d#† 64c…ŠÀ ‡ €H‰P ™ ˜e@‡4ˆ YG`XVPŽ ‡”`&pŒ0V‚€Œ$vX—Œ0%X€–Ž0€su0ŒHE(`ŽT2#aˆŽ0– ®œ2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†oø(4@L‹XˆØY™9yY‹ † )Y6‹h†8wUŠü†$ 6s‹\Y™˜—•‘€Œ<ˆ†# ŒHxW(`Y™h6sF‡a'X2e0ŽG•‘ƒpŽ$7uQˆ/ˆ0'U @Ž<4i8€Ž‡_ (WŒT i†l!Œ ˜g’$˜e0a"Œ<˜c&SŒ0˜a"D‰DŒH˜Y6sPŠœ˜†§ŽT˜ˆwŒl˜S$Ž$†ŽŒÌ—Š Š´ —”$ –< ŒT Œ”l†„†œ Œ´ŽH”Ì ˜”äˆ8ü —† “,†“D†$“\†0“t†<“Œ†Hx‘¤†Tˆ†kŒ´™˜—•‘€ ™ ˆ† ˆ 8wUŽ )†¢#pŽ9yY@Ž$Š,Œ0 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†Uø(4@LRg˜p‡#Y™– – œ2Cg‹0†0E@7‹TY™€ƒ V %gX$0ŒTvRb‹lY™0d†‹`Y™ˆHi`ŒxGgxŽT !ƒŽ0rye‡ Y™6@B–PŠ i†6`Œ g‡H`€Œ4y(’ˆ#†03$‘Œ0p8vP0Œ<8†8ŒHgC’Ž$[g95yŒ$˜Y‚•tŒH˜S2Y•Œ<˜R‚`•pˆ  †$2„s Œ f‰8ˆ›†b65ŠT ™8%"@Ž p3WuŠ´ ™'—”†w™4s’g™Œ`™d#† 64c…ŠÀ†*r €HŠ  ˜eŽ`†ö`XV‹ †F‡”`&Œ¨‡V‚€ŽvX—Ž<%X€P†h€su†43E(`Ž´2#aˆŽl– ®œ2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä†ð†wü ,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4@LP† Y™9yY@Ž )Y6pŽ8wUŽ$ 6sŠ4Y™˜—•‘€Œ<ˆ†# ŒHxW(`ŒTh6sFŒ`X2e0ŒlG•‘ƒŽ`7uQŽ„'U ˆB4i8`(WŽ„ i’˜g’$˜e0a"ŒÀ˜c&SŒ´˜a"D‰Œ¨˜Y’À˜†§W ˆ´Y˜U @€Œ S$PŒ†`Š —†pˆ  —”$ –< ˜†© W ŒY6sŽ$Š[Ž$ŠlŒ<Š~ŽHg†¡† i‡Ž$†TŒ ™’$†'ˆyŽˆÕˆËˆ$ˆæŒ¨™ŒøŽ<‹ ŽH"x†©ŠØ†Tˆ†kŒ´™˜—•‘Ž` ’À™’†J)†Ù™9yYŽ„‹4Œ¨ ˆŠõ¦`‹d\’e5‰yˆ” – š†ˆ Xˆˆ[Š Remark: Show this anlytically. Ž' ˆK Example 2.\ŒA (x+2)^2+(y-ˆ=4ΈuA†gΈn† ŠˆŠp(Xh†† `s‘hƒ@†`%ˆ‡†Sˆ0†йDvŽÂˆr† Ž ˆrŽkLŽ'‰C˜ u˜x˜yŽ ‡-ˆqB‡=5ÄH! ‘7ˆJÆÈ  D@†Ð6–°† “‡uQ† ™uˆPG†$`†(†ŠŠD†9ÈÀ   -íëx^2+-2ŒCŠCˆIŒ<Y™˜D2f† ˜†E†ˆ2À@–OF†š@HŠaEš¤PUA†¼Y–I†Ç ¤G†ÝAHŽCF˜ç •&E‰ˆÆ Y•˜P9¨CH‡ Ř˜ˆUI‡6ˈ# Š—?’;`” – ŠdJªXK‡U•U–° 26‘tp#‹HaPuhGˆ› ™ 6‘q ™†G† L† Å@  † †F†I†M†'Ä K–"N†I!ÇH–"O†[ÈÀ@†jÐ6–°†qaPuhGHŠ| 26‘tp#Šˆ‚––QC†.†˜ KW–2g”‰fŠ@P¢¡ˆ,ˆ‡ˆ‹Q†q.ȘR†3”ƒ†DŽ4ˆS¢0ˆˆ4T¢Jˆ4ˆˆdˆ<ˆ"ˆ@ˆˆU‡!1Ä@!œ2ˆPˆæV‡fÊÀ– -íëx^2+-2–•Ž ˆ0¦ˆÚ‰a‰i‰¥‡±2B††† [2† -3.044445151Œ-0.5 2.887509543Œ † 4897959184”'76420461ŽŠ'Œ%367”N6585292šN6938775€ˆN5†N1653Ž:Š'ŽL3–œ47801798˜œ’”Ã3†¯82899–'Žs02”ê 322826416–'28571428ŽˆÃ25164573˜'Šæ346Žb‰8183†b61˜u08163265ް‰_11870707—8ˆ¯‰^þ -2.056039352 -0.38775510’ 1.995448424Œ ˆ&Ž%0ŽŠ'3666736Ž:Š'†469388”N 879471899–'571428†”u8236707›ŠuŠKˆŸ”œ 769098183–'vŽbˆÃ71†ê9076–'26530612–ê66307†ìŽaŠ'16Ž*”N61137841’¯†'ŠJ44–t‡\415šÂ295918‰Œ †M‡l090‘I‰]‹ ‹”M4‡©1179Žû -0.2755102041 -1.41099718Ž ˆ' 653061224”' 362067023–'ŽM08”N 313445597–N 448979592”N†b05986ŽaŠ' 346938775”N216838†+–'’O”N†&71153˜N14285714ްˆê1206093aŠ'ˆ¾1632ް‰0724616”¯0.1Œ™5$ †M0241976ކ‰618367ˆÅ–Õ97574443š(Š%†ê7ˆÖ92‡[6‡<—_ˆ—‰­ -0.8779634832 † 1530612245” 8284726494–(42857†9”< 778463228–<1326ŒS”P72783725šx†s489†‘”P 6764867528Œ †´1Ž)Žˆ; 624291512–³ 1020408163”O†¯11451Ÿ‡ 0918367346–È 516798247˜)ˆLŒË•-46115†¦37–)‰‹–{ 403965459˜)‹gŠô•W34‡f4698ŽŠ)5’Ψ-0.2837326024†040816†53Œ ˆ) 198329558” 0306122449”( 152505707˜Q2’S– 804638348ŽfŠ1’,Œ-9.950126459îìë5Œ¨0\Œ± scatter plotÔˆÅW†ÉʈÏ|N&!`%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H$ ˆ^<l‡P_P†iŠ`dˆ°ax˜† bŒœ† d  ’de´†´ˆZŠË è’´•Ü ˆ¥Íð!‡ŽΑ!ˆ¥Б!ˆ¥ב,!•@Ø‘@ŠÙŽÚˆ/‡@ŽÛ‘|!‰r‹ Financia‡U Format ††† †Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– 4ˆyqYtŒx3Pcp‰†Ù ™–„!—’G †ñ —’éY–$œ0™ (1…0qy`ˆä#Y‡uYƒ‡9 ˜–˜œ˜H®Æ$ÈH •&E‡ %Y•ˆˆ Žœ¸†’ – øTøÊÌ2Œ¸†¼‡v†â$j<†H†T†`†l†x†„††œ†¨†´†À†̆؇ªä †ð†iü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†ø(4ˆx@†LDE`ˆu T0Ž vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A`ŽT%Es 7ua$‡``95 Œ„™THBŽx“fg6‡”q†L‚6pu0v˜Ž´qV Žxf0tHPŒØaxAŽäV’<Qˆû†üFy0A —6 gˆ14EYކ)&PY† !h8Pl‡S8 7„$aiäA—i†’ utD6‹8Y™ 'a4‹€† w–4ƒ‹†(G&I‹Œ†xF2(ˆØ Y™'ƒrS ‡- † vHgR€‡-$)PŒAqE y‚GŽagcpŒ<–TYŽ D”F˜ŒTƒs&@Œ`ƒ)UŽ`RPW†3"cƒH0Š„˜ •&EŒ<•2†›† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†rü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†aø(4@L‰c‰g‡t‰yY† 6‘Di8wUŒY6s€H—•‘˜ˆ#°(W(`Y™†"FŽ 2e0Œ†+ƒpŒ$‡uQˆ/†0†N @Œ<g4i8€ŒH†SW‡yF“‡uPŒ`†_“Ž`&S ŒxˆkŽ„$IŽ`†wg†…qB…Ž„† ƒŽ`e0a"ˆˆ†.D‰yYŠ.›w†>"$H—•Žä(WŽäˆñŽä†³QŽäƒ†Ùˆs†Íˆc†ÁŠË$ˆ B†©D‡Baˆ "†‘h$H˜ˆ4ˆyh •€˜‹˜˜”¨˜†Á¤˜‡~` Y˜2e0† † ŒÍ)†ˆˆ`Œˆ Ž$ŠŠ$’ ” 2†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†wü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†$ø(4@LDE‡ #`ˆu T‹$† -vBa@Že…)$VBSpŽ0G€˜09y‚‰ŽH2(&A‹T†:.%Es 7ua$‡``95 Œ„™THBŽx“fg6† †lT‡”q‰Š ‚6pu Ž v˜0ŽqV `Ž$f0tHPŽ0axAŽ<V’<QˆSˆ`Fy0A —06 g†s014EYpŽ„&PY†@Ž!h8Pl‡S 7„$ai´A—i†– utD6ŠØY™ 'a4ŠÌ† w–4ƒŠä†(G&IŠl†xF2(Š('ƒrSŽ$vHgR€ŒH$)†²qEŽ0y‚GŽ<agcŠÌY™–TŒˆd D”F˜Žƒs&‡Aƒ)UŽ`RPWŽcƒH‹€Y˜ •&E‹¤Y•2† $†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†vü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆÔ†à†ì†_ø(4@L† Y™‰yY@Ž † 6pŽi8wUŽ$Y6sPŽ0H—•‘€Ž<ˆ# ŽH(W(`ŽT†FŽ`2e0Œl†;ƒ†‡uQŽ„† j Ž„g4i8Ž`†SWˆF“‡uˆ6sF“†@&Sˆ0ˆkˆ.$IŽä•‘ƒgŽ„…qB…p ˆ®Y™†Z Ž e0a"@†ªU @€†ªD†Â †ª†jwPŽ<$†³†¬†­0†¬†¥pŒ`†{Qˆk†lƒ†—†¾s††Æc†‡Ž„AS$Ž`B…qBŽ`2†Ž„"†‘`ŒÀ$H˜`ˆyŽ„ 6sFŒœ˜†Že0Œ0˜”¨†djH—ŒÀ˜†ïŒT˜ˆ¿eŒÌ˜†IŒÀ˜ŠØŒx˜–lŒ‰O Ž ’ ‹a¦`ŠÈ‰Œ —’e5‰yˆ” – š†ˆ Xˆ†[Š Ž Example: Another eŒ Œ)\Œ1 animationΈˆQΈVŽ\ŠwVYrq’† `9ef‰•Š ’G5‘'† @ˆ™Š ŽDˆ³v’K†r† Ž A† 'LŽ'ˆçC˜ u˜x˜yŽ ‡Y†Æ@  † †Z†ÁH"ƒŠG@†&Ð6–°†-D‰X’BE†& 4u„g€†Š <Ž [†Y ÈÀU–B%‰‚ƒ†z ™ t'pˆ` Y™•xaF23ˆ’™†3\†BÈÈ ƒ`Š…E˜…Ph¶†Ož…]†ÞÉÈ ŒCF˜È”7˜ùŒz˜C^‡!Ä™ˆ˜ˆÞ_‡;ÅH–ˆoˆ‡TˆµÇ¡Ua†‘ÉÈ!¥@"p„‰™h!G !R‹"77#5ˆ¢‹dˆFbŽ”†F†c†ÈÈ ƒ`ˆC@†Ð6–°†€Ž%` Ž  ™’ Œd†C ÈÀ! Š–B)€XB†6 Y™vuWHq•Š 4V3Q1І3]މe†•Ä@ ŽJŽˆ`b†1Ž"ˆ_†^†[Ž$fŠ:H–:\†gŠšÈ–Ü h€†0ŠÐ)#IX–ŠÜ&ifH49Šô†h"D™EDP” Ÿˆ‰i¢ŸˆYˆŸf Ž"ˆˆ.j¢Íˆ.k‡² ËÈ#gÐ6–°†R2—X€b† Y™ 5‡Y!‚‘† ™Gd‰T˜†*`†.c† h†l†;ÄH  † †Œk†QjÿÿÿÿŽ"ˆˆ.ˆm†m5Å@!’2n†DÄÈ ŠDA@”Šn†&6†¨ƒ?†½o†ÂÊÀ!”‡-(íëx+-1)^2+-4˜H«ˆ×PC yHqyHr‡  ˆèp‡Ç@–Ûq‡(ÃH©B¤©–©ˆ ¢©a†ˆbÇH–­ˆYs†ÃÊÈ‘—h!G !ˆª ™@"p„‹” V ”t…†q† t† !Ä@  † †s†aW–2g”‰f€†u†4Ř'n†a††v†R.È@ ’w†d3ÉÀ!”oŽ4ˆ_x†‚.ËH–0ˆˆ4y†œ.ʘˆ4ˆˆdˆ<ˆ"ˆ@ˆˆz†š1¢šˆPH–vžƒˆ·‰c†h†k†\†g†]†[†d†Z(ˆAm‘$ [(‡L -0.5229403823Œ0.8” 3946122586Œ 0.8179487†”E 264952635Ž;ˆ'† 97435ˆ' -0.1338658196† 0.8538461†Œ-1.252210698îìë3”+71794†Ž+†> 1329899095”Q 897435897’d 268966744”& 907692307”&4067†ž94”9 925641025ް 0.546562241’Â9Œn43”Õ688409†˜4’„9Šäˆê”û 324496012’ã9Œá7–Ð978805‡•49âŽ_ 1.1276045- 1.0œo†2789807‘iˆ$3333†”643‡006ޏ 1.051282† 1.590014988’ 069230769’$74996129”6 087179487’H 913061434’Z1mŽ2.0†372246’~1Œj23’$24935616”14102564~ 2.42288213”´15897435´2.600†j522’ê1Ši07´ 2.78156478¢1.1ˆÔ†Ú”´96709031”´2CŽ´ 3.156‡!’é1.Ö³ 3.3514836–³2Œj4³3.55‡v341”26666†‘g3.755053048 1.284615385Ž 3.964578506’$ 302564103Ž 4.17957508”H 320512821’$4002871˜H3Žm’H62696877~1.3Šj†p’l85988425Z 1.374358974Ž 5.099308679’Ø 392307692’$34552861Ž$ 1.Œi4Y5.Œj33”k428ŒÙ’k85956060”³4B4³6.‡ 00†¥‘11.4ŽÖ޳ 6‡45209•f4Žj² 6.68945373œ 1.5[\ŽÔˆ{† ÊŠ¨N&à%FinaFormà$N†Graph2D†% 3Š ˆLISTSYSˆ$†@4ˆ< Modify XˆPˆ<STATCALC |ˆdˆŒ< „\ˆx SequenceˆŒ,ˆxSheetˆO |’ŠŒˆ’ olveEqˆ´†€`wrˆ´(Upˆ’tupFLG1 (Š<†Lis†{HD‰ˆPic†ŒÜViewWind°ˆŒ_osve†v‡5Ìx䉉،ä’ä ä’ð´ä’üÈ䈾‰g ‰ †ä† † ‡<†˜X’ ’’,’’8’’D’’P’’\’’h’’t’’€’’Œ’ˆ¾Šß˜’!’¤†"†°†#†¼†$†Ȇ%†Ô†&†à†'†ì†(†ø†<)‘† !*‘¤¸†ä+††  †,Ž5-†4†.†@†0†L†1†X†2†d†3† p’ˆnŠ£|† 5†ˆ†E†”†F† †H†¬†I†¸†J†ĆK† Ð’ˆæ‹C܆ M†è†N†ô†² O‘|‰…ŒP†Å †Q†Å‡R‹¸†Å$††À†Ô S††ˆ±T†C<†]’H„ ˆ^<̇P_PP†iŠ`dˆZ†faxˆãbŒ\† d †FŽde´ä†”Èh’´•Üt†Íð€†ΑŒ† Б˜† ב ,¤’Ø‘@°† Ù‘T¼† Ú‘hȆ 8Û‘|Ô‘ Financial‡ªForma†¾ †††Œ†ˆ˜ systemä]Setu’^äa† _LIST’`Œ’†,ˆ†#bŒTˆx`=@ŽŽž¾ þ@þ€þÀû=@`œ ÿÿ@ÿx‡¸Ž=®Œ< W£ˆº%†† a‡ MatDatab‡*.EAC‹1‹6† ”¤ÍˆÍ †I —p† ††Lî<‰¼¦-^††ú Œ©@ˆ Œö<ö<þxþðÿ,ÿh§¤‡‘9’*‡Xc‡p†† †Œ&Œ,’ ’,† †0†!@†@PSheet1|ð‘|:˜^Š2ž3ž 4†5ž ä8ä7Ê|è–|œš"˜|†$ “i™” ™‰G‰K† "“-ˆ‰l^E ‰eŽÀ‰`†$«d«y‰´†`†††°† Š” †#’$†(œ†AŠ ˆ'Ž `– PZÆ$´$’¡– W&DŠx8–Š$–„B˜9UW†ñ ˜pê ™”`˜0™ (1…0qy`ˆä#Y‡uYƒŠH–˜œšH®Æ$ÈH%"i€‡/Y—qyHqŠ  ™ˆˆŽœ¦’ – àHàxਚ(Œ¸†¼‡~†ê$r<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Oü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDtÔ"”‚0‹ ™”a"X`‹¬™d•&5‡¸ Y™3†X`Š %"i€Š —2˜™ Pˆ ™h–gDŽ xe”pŒFV"Aˆ;†$ˆ@™@Œ02D– Œ< x€QŠ`†7UvSˆk'‰€sŠl† C0pŠ<†Y˜t™a)Ž$‘0aCŽ$”r$Š´$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÌˆ$–p1Ž<i–Ž5ƒcˆ$UcAŽ0uPSލ–ExPŽx•uŽÀ@‡†0ObihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ( † ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ†£0 ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i#†}%d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( QŠx †P#†ˆо $‡”†¹&fffpŽ(F8PŽ$0†¥0Ž02†u<3ŠÑH5ˆ»ŽT7†»@Ž`9†m ŽlAVAˆwˆxB‚†DaS„&<F†%<H Q(<ŠŒŒ´ (†† ††$†0†<†H†T†`†l†x†„††œ†¨†´†À†̆؆ä† ð†Nü†† †,†8†D†P†\†h†t†€†Œ†˜†¤†°†¼†ȆDÔ"”‚‹DY™”a"X‹,† d•&5Š3†XŽ%"i‹\Y—2˜™ ‹Œ ™h–gDP ™xe”pŒ FV"Aˆ†ˆ@™@Œ$2D– Œ0 x€Q`Œ<vSˆG '‰€s€Ž C0pŠ<†Y˜t™a),Ž$‘0aCŽ$”r$ŠT$“VŽHB(‚ŽT`$RŠ„ˆxdxŠÀˆ$–p1Ž<i–Ž5ƒcˆUcAŽ0uPSލ–ExPŽxg•uŽÀ@‡ŽbihwŽl…˜„%ŽÀ “gŒü4U(a YˆB3Žä…•``ލ€C0Œ`@E –8h”SsŽÌ(† † ††$†0†<†H†T† `†$lx†)„††œ†¨†´†À†̆؆ä†ð†Nü ,8DP\ht€Œ˜¤°¼ÈÔ† ™”‡Ž 5‰t5 S„aS€Ž$qyHq †#‰pŒ< i# %d%`ŒT CX—C a†IPŒl †Gy —†%@Œ„$3330Ž ‚Ž’0vЍ†$ˆ‘Š„†0Q( <0v’<†’ŽT؆`´†l†x!( Qx#†Ùx$‡”x&]fffx(F8 P0%d0Ž 2‚Ž3„aS€Ž$5d%`Ž07CX—@Ž<9#i ŽHAVAˆSˆTB‚<DaS„<F†%† 6H Q(<ŠŒŒ ˆ®`VŠi†Í ˜’e5‰yˆ” – œ˜`†‰XˆŽ†’[Œ eActfH x1-à(1-x^2)f1H xà:(f(x),x)gH$x-(x+0.45)^2-0.975g1H(x((-(20*x+9))/(10))h1H@/x((-à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))h2H@.x((à(-4*x+4*à(-x^(2)+1)-7))/(2))+((1)/(2))0301cb00200008000000001ed1xœíÝ}ležàñ®vû¥:¶d&3cÀ@›´C½õÛlæd6/$KL^"1ÁÆqkÇÄ8{yfØÆdBÖ±BHF¡:±'´‡Nщ?ööÐjn…n˜§[Ý »£;NjFºâ½Õü±‚û=õòTuu{HfÂL¾Ÿ™²«~õTÕóT=õÔSO7±ñ£ãGÙ1ã¿§Ô”êNy>MH}AÍžš›<–JÉ9XH=’JzâÄø‰S²<0ªÖìÙú°“JùË«üeÛ[.t…ë­øòÎ6ß»Ó5—jb¹’X.'–K‰åbbÙM,;‰e;±l%–ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù³ù«&®%±\N,—ËÅdýI,;‰e;±léåË,³Ì2ËŸïò±ñ©éøòȽ£;y`ÏýÞr[*µmjz|ÛñÒÃèxOVîN¥j÷Ÿ9bo‘ÅŽåGÿª0æ¨XgF~t«ØÎ{÷íÝ¿WÅr’ÖUÛî:~pêÐ)u¤•xP¥Û»ïÞ}òØ,±#ëÚÄüm{fR©ôc^lòÉ““Ó“©Ô*/oÛ#““s^‰nü•üxFǼ¼äætìøÑ§&·>©b*Ï™ö0¶óéû'•g#Œ=4#±5)›;9³mç}ÒMZ£z—ùö ¶sjVö¿Æ•Ø–UAltjBÅæÃ²=<5ùô#SÓ%öŠÄÖ«ØãÇgŸš<¡v¿æíð³G¦ÍÝïÅ~(åõÎ_=^­¾÷Ãtõ5:ösëÕ±_èXŸŽé²ÕûÃX¿.[ý&ëÖ±›ul­ŽÝ¢cƒ:¶VÇL[§c›tì+:¶]Ǿªcûtl½ŽéØ×t쨎}]Çæuì:öœŽ èØ’ŽÝªc¯èØm:ö†ŽÝ®c—ulPÇÞѱ;tì=»SÇ~¦cwéX]Çò:ö±Ž éØ¿èØÝaì¦.Û cý:VбÖ±‚ŽmÔ±ŠŽ™:¶EÇ,Õ1[ÇÓ1Gǎ蘫cs:VÔ±Ûªcgtl›Ž]Ô±í:öºŽíб·tìOtì¯uì~{WÇvêØßëØ.ûPÇvëØ/uìû•ކ±›3:ö ŽåtlŽ­×±½:–×±}:æêØ·ulD~d¼6‎mѱÇul»ŽéØN×±Q{BÇöéØy{Tçå%;¨c?Ö±û‰Ž=£cïëØ¢ŽýTÇÎëØÏtì5û@ÇÞÔ±Ð1ÝžÖÿQÇ~ƺ» ïy6=15®õ\—Úi¤²2©ÿË”–B§¼)îA­‰Rá;·º{'çNêe¹êœêe¹ê¨—Çü˜^÷czù ŸÊØ·FøÍo~ó›ßè¿£gJ·zäîŸÛ2>7žRÚ[ïÝœŠ[Í^és&v<#œ~ÃmSlûÞ¶=êÛÈÔ¥ê£Lú-³A‡N›“i@&S¦™F½÷k+õÌÇçžùæÅ)oÙN,;‰e7±\L,˱êò6R/_ѱS¿hK¥bÇn\vËnb¹˜XŽ[dõI˜ºͯ»”2 ÝM”yu[‡—#ø}à;©ÔÖž°óœßµ2é7Ç+k3VLÓÖx=W…¹“Ëû••ϧLc2ÍÈ´ Ó’L¯Éô–LïÈô¾LÊôqFÊ(“loÈö†loÈö†loÈö†loÈöÆÒU—¿Smzn,6ŸK¥õûkÎø­ÒDóFg|~&JÍçôÓ8Ÿ½Ô¶ÛÿBëôqyëÏÍ'O©xûíûŸ?¹ÿ{j?cù‰ç­a?í+įUške¥cý¡[é\Eñ±ÆºÑÓòdñ…S^ÝÐó¹ÔJñøþ7ÔXPå¡Tê9oìZÑxMÅvl~`÷®­»¥Æ§_“`÷n›žšÛ{jVÓoJ{MÅöœœžŸõòµSm¯¶UÏc¿Š¯Rc-G¼˜WöcjxüØÀÃãGONfóòj8qÓ=~Bõ=ˆøv^¹³ÞÏï98`oÉæ½¹¡BýÎgë u³P· u§Pw õb!È>d™æP!ïäËLðiÀP«ý9áþœ-²G»ÿ3køÏüíƒ Tþ¶;yìØø‰SÙü¬?­W#éj(ýøÓÙúWž­ß^¨¿_ȇãëÇŸöN›Òª<ÔsÏÖ×ê?}ÖòÓlŸ˜;~"[,¨1\?¶oü‰£“Ùú=…z¡P.¥þºÍǧ§&f¶>™­?ÆÂO$²õû õ­…ú¶B}{¡¾§Pß[¨ï+Ôw<[°Ÿž˜Þ`K™g'Ÿ|üÈÔ¬œÝ|¸eòúÄë~[FpwÇ>ny½ÖÞî}Ürºßpdz»Öot/öwŸ´,ößøÃÆZjÔ–êþU-o .nêŽ}β¾öѵ˜_ì?³©£gP}À¢ÖGŸ¯,Ô6…ÅùvïâÕNKFn|SŽõÌrÿé3é\~¹¿Ãÿ<¥vÙÈ-^NgÚ—$Þ')oÔ~œî6–òé‡fûËËý«õ§'¹wd¯ùÓ›jým;§fkÿ:ûEí ±å…ÌbÛèÔDí/Òk K?ïŽ}d2*Ç\¿x¦ÝûĤö”dcÍÑ¥ùt=wú¿<¿/½f~éLº¾f¹ßxnéµt½Wf––.§ë}2óÊÒ»ézÿrÿòÏÓõ›ÎìI­‰†ño®­ªõ¨}½# o‘é=™ÖÊô3™ÖÉT—é+2},ÓWeú™ÖËq{»dækrÐ^Ù³ñu9hï€Ì|CÚ[Xî_üúé¥{+¹uéçéÞ-2sÛÒÇéÞQ™¹ý\&Ýû˜Ì ž[›î="3wœ+¤{çdæÎs#éÞ™¹ëܾtï™ÉŸ;’î½(3CçžI÷¾.3wŸ[J÷¾%3νžîýëßî ‡ûk™¶TﻵUmR69[Ã’æïeÚ(Ó‡2™2ýR&K¦_Éd/L÷edÆ‘òôådÆ•òô­—™¢”§O.­±ué²Ñ·hŸé7¶ÉYì‘Ðv)PßN™Ù!ê{TfþD ÔwPfî—õÍHé·}ÿžtŸÔc—¨oQfvKúÎËÌR ¾×dfT Ô÷¦Ì<(ê{[föHú~(3{¿ÿ¶z¨õ½_kï †Àk7Öz3ê“.Yým™~QNgVIµ:”êñà"ÉôO2¥|"¸hç—Îýµ×Ïž1^’ÂõwKèÇr±úÕÅþ‰”­PòýNÿ¯t¿:O?•²õoRõ@ÊÖ¿]f>8·Öèá69ÿp®`HR™ûG)]ÿÑsûÚ½.z­¿–YìÚ´8ÿϛޛ_{ñ\ÌÆ™:üÖÅõ]Ñ:ƒ7Õ¥ÞôÉü'—?ùøÓB‡ÿŽZËÖ2F¦ÖetÉÔ]˹Ͼx~yµÑ±\0rÉ”i¤6’Ý›K¾.æ ûÕœá¼:`¸2_P¯qþ+^-›Q¯—µN9D㮤vž.tï–žy¥aŸ©ÍÙ3µåôÔ¥óÝYý6X»a±³MÞ—óµ[NÿQ‡ÿ¸øŸÎ¾#ï2ÖÖn4—7,»ÿ¦÷•\íÛ‘1ºÿæç3gHñòF×+_]zUлÎ|– ÛÝå÷QÒ£‹]§»ÓFÛÒê6éÊœïþ»ÁÅÁófÚè¼Ðîœ9¿ï|w›ôj.l:ßQ=å cËݯ˜K«ÿ¶+ì/¾×ô‚k¤³/,]|åÛö÷Üß þdûþòÿñòWß(þÕåŒß‚œé¼ØóÖº­OÆÿö5ÃXî6rµÖ»0¸*êk-®=/á ݯ¬½8&Û<>£Â¾„ßÊÞ;=;°kòØqõ¿w÷Þ][w éu»Æ§¦¶ËãÏ[»]î‡=û½‡v°~òÞ‰¹l^*Þãû¶î¶»oòø±É9µÍ}[H¬Û2uè<’üÇq~ËÖÃÑ~7šyâøøAéíÜÛvï̉Éñƒ³ªòH/eo´a°Þÿ¨H:SÛvìÖ+WêKy}¾¬ÿó6ÿvy,üŽÀm…xD}C 1¢žŽ·I— èæyyXñ8ê¹›Ý}òØä‰©‰),zKêºÊ|úßµˆ2t'ÔÇ⪚U?TI>{“BýÛϪϱ¢íöLΞ<:—­O꟭Ÿ,äwLϘ?ºùøÁɽMeUÞg #6zSñy©XOûß™H©ï¨ïoêÂz-–ô§eÊK·Çê—J']zã]¹× Ó¯¬FÚ{øZ>8?14|(??4tO~bX~Ý}Ø’Ðë[f›÷ù¬Ÿ²ÃªÜmÍ=ÞXɸEÓÜã%ö–:6sTzZy£Í¥`•ag™Ž`ó2Ãv¸vƒÞ Ò¼Að{È;ömÞÂêâFÉŒe™·Ø~‡‘{nû¤×Zx³“©äía½— ˜:Ñ„o‡Qê–£Uaê–; ‰¥7Ø~ñc‡K¦i̵»±T)ÙUK²ž9òĹÑÜͱ\7åTŽíÏu:-ËÙrýü^I:}Ù|<3yfòÌä™É3Ó`Êfª¦O}Ù(þÌTc`ïÞÇ/<3¿ŒÏÌTÚ=•_öæö_ú÷ÿÛ0ÖH3ÝŸê—‡^:í ž[j¹Ê˜©<5j¶^U©UÖæZ¯ê<¼y¹õ;W‹§ü^L¬ÊìÿîKþ iÓ*c¯½ÿ¥Ö[{¾;ö’7$›mÞ¡ýÜì@ËU‡^HUR-WO”Š^æ³ÍEþη´^5ãÖç¾*e7\MýùZóÝW=µíHëUCû×–fZ¯ZWyú¡Öw_:»¶4;ÚúƼøòKçZ¯Z”ý ´^5ÿH~¬õª#¥Ùm+4ÞlO®ÐtÜ÷Ò¹ïµ.—Q>ù`ºõ‰2î’ ¶>QÆ-îTe…ruöçi}¢²Sú&®Ãz‡MMǤ9î7M«:&îÜÛÑz‡íã·my¡õ3ûõõJ®j{Dg>¹*­NFë{;z[ï°]6úŽ)_nµÊ¿“«¢6µ–Q6šVy™h¹**rÓªèD5­ŠNos{®.JëF—²iUTZ<Â3ßÜÔëÊÖ¼JWÑæUºb7¯Ò·Có*}5¯Ò·^ó*}Ã6¯Ò·yó*Ý84?Œt“Ò¼J7DÍ«tóÕ¼J7zÍ«tS4¤êv*­{Œ®[Ë5U1™_WîPó¹T›þ6ö_Šæ³—R~?9ý§©Ï°^e‹þ5ýë«é_ÿé™Ë—¼èìX:]~§íRzÝò’üª}ðbWÇ%¯ÂŸ}ÎHß=óÆÒªÅÃXºÅHþÿvmÛXªýû_|¬+9¸ðƒµþj™ð»|Çc¬±†ßÕXƒúokbL¯Ò+â»rß}C~×ï‹y­´a|]5¥†±Z~%ºÃ{_œYáñZ¯ê²7δîlvn)¯kÝSîXø^öáVÝqøÑÁÖÛö§Öíy¢ug³Ý¿UŒG0ÁxãŒG´\Åxã_ ñÞ]ywåÝ•wWÞ]ywåÝ•wWÞ]ywåÝ•wWÞ]yw½Þß]¹¿ÿkðYëZ Z“Lwßjh¼,«ï%dºé¢/7• þ\MFÃÌ€LÒdFd’ö,3&“´„™™¤Íμ&Ó[2½#Óû2}(ÓÇj߆l/Ó€L¦L#2Ê4&ÓŒL 2-+çׇèß¶MÅæsÑÃÍÈýViRQšÎøüL”>6Ÿ‹Ý ±ùKÙèßÈ•ý/´NŸŠ‰þ½ÜT.ú÷r/fÓ±ôñùø~ÚWˆ_«4©kd¥c]«ýÿ¾¬t®bñ±†º¡ÿ-\©Ñ|n¥x|ÿÄöýeþî–þ;y)¾ÃÅ88ãàŒƒ3Î88ãàŒƒ3Î88ãàŒƒ_ßãà‡‚õ“ÕÛ¥: þ¾ïÅXìpNý!ÕÁ0¤Sp:ÄŽ±ŒáÿãË^,øÛÀ[b1µ|C*G™OYÃ.å­áùvø§Ž{ÖøÍ¼b/ÌG ¹aýp~~ƒ¹Ñ-°‡ÍÕ²ÿG…ojH“Ïçmóîù U5To™Cz_÷$ÓIf†]IéÞ­ææäí¡ ÖÐpYmh mÈç-Îßfcbû«ÙœÏ"¿šqpÎÕ•Ÿ«å‰ eÛ5Í®DÞ¤†û¸±hÙŲe›ÊGËaJ׋ŸµJÁ:#±›ÜËuýU‰Ãè;AÆ)«®U-Ú‡q~»ÃͲ,Ë­”KŪÝp ûš”g8¼³»Ë­V+Å’·Ÿßf×úŠÈ^äª4í©EÅÌèr¯.¹fòÊ…TÏ«lWÌd†ŠáÚ¢]uÈ®{¸¾T¬˜•2ѳ¡l9®Si]Ø›78vÕ´ªnÅ+¯c»•jÕ¶®U ÷b{»i¸Æ_îSÔt3¬v«Ž|IÏHò„tYÅRYàK|6¼»C·gáÄö6¨®Üâ­rŠ–ãÈc·Z½í]zƒ]œ T®3®úYÕµÒ¹¼Š|4=³–YiÝŒü&{ ÏVÖvK%Ûßtgræ?ÔjúÔ´«8AÉšÓ^®8Uó7ØOF7™ÃÔ3êÙçVÏVlü¾Ì \ÛðUïó®z~8£Æ?üwÍ`w³êò »íãÓ³…‰ØXȺ­{ö<°ç›;¦gO:45159=|¥!ù~ÉØ c7W3ñ¥îxóîÊ»+﮼»6žË/b׎w Þ]©g_ŒzÆ»+﮿Ÿªç‡ywåÝõºxwåüþ¯÷(õã×ÕõØRß6ó¾c–×ÏšygH¶ÍÇÓò¥¡†'ó|q¨áa| ï5<}Õn¸ÞÛZ>cU%‹_}®ññåS©Èõ›ÍØ€ÌõšÅpˆäºÌŸiÕW0½–Îç£Á‰+.©¥ [Vé]ÓÛ±TöxÖÕ×;í~¼“eÆÊvE[è~óg§–rýN/B«s{Eeò:§ŸRíÌ;'ús>ÑÁ—…¯Ç:=ñ…;ÙC^÷‡~Ò—¬Ÿt½ÿw…lc_ÿH¶¹¯¿”úúÒTä'doê‰h‡È°Ü;rK¦»_+WÓŸ¨ú]3¶|UݺRÑ-Û MÅÕô¶\§4a»r['¾Õ­¡«Ø:ñeí õ½âNXã7°ƒ–øŠ¶V½¡Ø«¯â ôõéë_Gù£¯ÿÝ+¢¯O_ÿ w²éë)ûú«ä/õ ›íŠSvì’i»~쉙®)i$Ztb ­jEêi±X‰b¦c–,ÛvÝj³Šr)Še³ß¡­w VL·äT·âÄ‚–Në× W7VåÙ%·Xý¨í—ÿ7ø”Ô??tzf'Æçæ&O Ì=>×Ó³u~\jÝä7î>>wD“~ §g|zêØøÜÔñé£7'oé(ÓEÛ®º¦S±ƒ£¶™cÅtª®*f±ä¾[ÖZe¹_ËV9VrÉ¢ôKNx†T2Y¨–]§?AŽS‘&ÁªÆöVt*rùÚ’ mÛ–YªVT¡(i98rtK.‹´fµ¥ò*?uÈ.Uª¥RÙu£TU³\ªÚŽYŽR¹¦ô¡¤§îF¡ª¼0¹rYŠA~WËérKÅ’\w+Jä% UªT\³*ùr£T^UIcgHUŸ’\à(Uxjc9-W*fQNG´ûjXÂ`÷«¬–].™nXiW[R›'»\‘—¨rx¢U' #®tÈʦYr£4òöT±å§Ž«¦)ï%•Ø~üSYªêHY:uRoªÑVfxõt¤j©[Èu¢cYáÁ‚ˆ½Ñ”MÊr¶KQÿHam•4¶ôÏ‹%«åÇò¯Yx$kÛ•ŠmÅÊn5ÖNI#O 9’T½(Mc‘4åŠô´Ýr%:«Vã“4ÕRÙ¬šŽåÙNaçU޽$'ÈŒ]œ Ta–Ò;–æ¡˲í)lq$M±([9nü"—|e¦,‰ŠŽéÆöÜpE¦*-ŒÊŒ²ìø'Ð O³»Q•±\4c—ݱýëeé4òlµ%ñý4ÞݪݷKÕR¥\Žòì$n2W©^®«tNc—§žÜ_òòP*G•Î j¡­Ó8n±hWJVUß'‰šQÜèÉq¢C¹þŲ+:dGÞÁã—ËuƒÛ9ˆ”¤^J¯F2»—‚R…7iINT/³78’­w#-•ÜÅe'8T›ÜnÁ\OOOÊ òÅè‡è'¢<Ù-¹Ëõï–ÆJ^åån«Äz ®ô‹åþ«êGŸ$s$R±åéKæ¨Kv,™4}òxŽw|¤†Ë–ü,EÉäfS€OæçÌ Ûu•LBr}GyÉ=&/™U‘nîù= ¿N9JfÊmåHë­³+É’%Eµ(åwíøÎ‚Dú«’9ªÝsJv,™Ÿ}§R‰’UÔ#Åj8mŽ6äg,™-›åb|oÞ®Ô‘£dÒܘՊ¿VNxÔj,™4ø¦êsÄ’©3æõ!£d¥’4`RÖb,YpnÍR,™e9åŠkY±ÓÖØU©äˆòdh(] «[Ðà¨d–)93c'7¬År´3W.”=æ¼dá%ˆ5iñ¤sbU¬X²°˜±K%I:[¦ïc;3c—Ê‘—EiÁÞœ—,¼bgMŽ`J3^ŠA_«X2é"ÈCÏŒAï.J&©Ê–4îñ½µÃubɤfÕ)Ç÷öôcçÍ”Né›Tc5Ü *‘]y±ªºÿäõ”Ã[/–j¹(•Cú™ñtA/ÇúìU[NmI½hÇÒ…µ(ve$Õ’z‰Õ+¼X±rI##0éáÇòž;–—²ÔÉ’jnbÛZºšÇÒIOÔ)Ûņ㆗"v‡”Ê%WðE»;yAÂXqK¶«pËŽ6ñ*å½è”Õ`|Ñ ³ç½sUmœ—Ð*©–Õ-ÇV÷¡×òÉX”\†Mš—°œ¨,~éTKEW×d/aI—9ÞÄÈY–ÌTª±„E]šø=Ê»+ï®:Ä»+﮼»ixwåÝ5˜ãÝõóùÛ;œÏkx>¹ß¨¿®~Zúÿ! Ÿk04ac