00020001010008main.ACT000202000cExp-diff.EAC010000001fc2  Exp-diff.EAC main.ACT),0 $ ^ '>[4+])onential functions and Their Derivatives\3 AuthorJN Wei-Chi Yang Radford University / e- l: wyang@r2.eduE!URL: http://www.#/5ݎ Objeve:[WWe will explore thhetcorres4ding d with ClassPad. [[ Note. We will explore y=a,x48? and its corresponding derivative for 2  mPP\htȒԆ  !, "@ #T$h(%|4 &@ !'L(X  )_dc*p+|,-.012Ć3І}܆5EF!H I JT$ Kh%L<MnNT*O`ņ PlnQrxRS;]m } ^_  ab̆ ͆؆·І׆ FWّh ڑ| eۑ, FinanciaFormat  ! system]list^]=_`a "b~h/ @/ @x !, aiff(a^x,bXv>F PU Play thΈ `F5!  7H3D-vMrŽ AL  C uxy I R@ N-a8`shB G6+`!&0$x%@0/P<:R`HcxpTWI<&1W<Y 0 $<TlE vC @A %FG# $S %1R Y$B 9"tS X@ 2D` &  1vPV$)T/ @P(pH8D!0%t0d0Bx xbM5@  [_ At6E >!U2^xq`L`&1WG.H  @3Ȗ]o "pt"#Y 1W5t 73E3U3 .H\r \.H!      )1Ǡ2H 7`m[|Note.  Constructi  of y=2x& and the scatter plot.L8@?  above.[tStep 1-Insert a Geometry ip. "-Select coordinatystemH-Und 'Draw', s4fun.) -Type in tOr you can dragdrop 2x  to the geometry strip above.][&Step 2.2-Under Draw, select Con; uct->Tangent[a curJ:-Tapppoi"and~%'-EdiGAnimate->Add a ion->Go oncT3.[?-Sgony=2 'tableOYO 'slope' of&line anՎL This shouldwsoV`s4XNow drag the x-column of!point and its corresponding slope)tange+line 4 o CWgraph, we should seepsketchn'{ derivativ`2LxT function.[fSWest(x,y)oratՑ below:[-50.0312  216608493" -4.473684211' 5 450077043 31196963493.9:` 6482219028Z 0.04493131855 -3.421052632' 933599351 : 647121759: 2.89473684: 1344613233M20148695v&1936574534H191.7 2789144794L3287849315)47&401705L4411129 -0.657@56 M0238Qs8332620KK7578216&9 1.20_72 0.8318550617 7894736842& 1.72844378%198076=$315:4\ 2.489385179H5525Zf105263 3.5853289H51817786 5.16375679H7927445ن 7.08ܔG 376}3. 0.71121G2452495A# 15.4268159B 0.69314684.v1Y 22.2184115.4007676532 22.18090172\$ List EditorԈ7;A |N4FinaForm$NGraph2D 33 LISTCAL,SYSBE$+<h08Tvv؇P!BDDwqy qH7Nq@d %Bu 6$w'x!0xqE<xc1YHWT1b2`2PHg1wW5!85YPHghfTgI#d`5$`lA$xt َ `$ e5y  `W1[ Question:. What is list3/2 in the above List Editor?RC: Clear_a_z R\Pdone& t/2mx+h-xh0WExWlnc.a^6Ka[O Exercise 1.[8ApplyBtechinqt described^Example 1 to compare 3 and 3x.[ Exercise 2.[-"UProve that your conjecture from e4three is"rr" using traditional calculus techniquesAcknowledgement:< The idea of Exploraf 1 was suggested by Jona n Lewin. l eActa 020012eActivity Save.EAC010000001fc2  Exp-diff.EAC main.ACT),0 $ ^ '>[4+])onential functions and Their Derivatives\3 AuthorJN Wei-Chi Yang Radford University / e- l: wyang@r2.eduE!URL: http://www.#/5ݎ Objeve:[WWe will explore thhetcorres4ding d with ClassPad. [[ Note. We will explore y=a,x48? and its corresponding derivative for 2  mPP\htȒԆ  !, "@ #T$h(%|4 &@ !'L(X  )_dc*p+|,-.012Ć3І}܆5EF!H I JT$ Kh%L<MnNT*O`ņ PlnQrxRS;]m } ^_  ab̆ ͆؆·І׆ FWّh ڑ| eۑ, FinanciaFormat  ! system]list^]=_`a "b~h/ @/ @x !, aiff(a^x,bXv>F PU Play thΈ `F5!  7H3D-vMrŽ AL  C uxy I R@ N-a8`shB G6+`!&0$x%@0/P<:R`HcxpTWI<&1W<Y 0 $<TlE vC @A %FG# $S %1R Y$B 9"tS X@ 2D` &  1vPV$)T/ @P(pH8D!0%t0d0Bx xbM5@  [_ At6E >!U2^xq`L`&1WG.H  @3Ȗ]o "pt"#Y 1W5t 73E3U3 .H\r \.H!      )1Ǡ2H 7`m[|Note.  Constructi  of y=2x& and the scatter plot.L8@?  above.[tStep 1-Insert a Geometry ip. "-Select coordinatystemH-Und 'Draw', s4fun.) -Type in tOr you can dragdrop 2x  to the geometry strip above.][&Step 2.2-Under Draw, select Con; uct->Tangent[a curJ:-Tapppoi"and~%'-EdiGAnimate->Add a ion->Go oncT3.[?-Sgony=2 'tableOYO 'slope' of&line anՎL This shouldwsoV`s4XNow drag the x-column of!point and its corresponding slope)tange+line 4 o CWgraph, we should seepsketchn'{ derivativ`2LxT function.[fSWest(x,y)oratՑ below:[-50.0312  216608493" -4.473684211' 5 450077043 31196963493.9:` 6482219028Z 0.04493131855 -3.421052632' 933599351 : 647121759: 2.89473684: 1344613233M20148695v&1936574534H191.7 2789144794L3287849315)47&401705L4411129 -0.657@56 M0238Qs8332620KK7578216&9 1.20_72 0.8318550617 7894736842& 1.72844378%198076=$315:4\ 2.489385179H5525Zf105263 3.5853289H51817786 5.16375679H7927445ن 7.08ܔG 376}3. 0.71121G2452495A# 15.4268159B 0.69314684.v1Y 22.2184115.4007676532 22.18090172\$ List EditorԈ7;A |N4FinaForm$NGraph2D 33 LISTCAL,SYSBE$+<h08Tvv؇P!BDDwqy qH7Nq@d %Bu 6$w'x!0xqE<xc1YHWT1b2`2PHg1wW5!85YPHghfTgI#d`5$`lA$xt َ `$ e5y  `W1[ Question:. What is list3/2 in the above List Editor?RC: Clear_a_z R\Pdone& t/2mx+h-xh0WExWlnc.a^6Ka[O Exercise 1.[8ApplyBtechinqt described^Example 1 to compare 3 and 3x.[ Exercise 2.[-"UProve that your conjecture from e4three is"rr" using traditional calculus techniquesAcknowledgement:< The idea of Exploraf 1 was suggested by Jona n Lewin. l eActa 0301cc00200008000000001931x}l}B)NmiGM.Z~ȎbM<$hKȲbɱyfZQ\JU'02c0: cuִM(,{)j5M9>"s?Ѽ{¼4kU~p\b<695|0d07st_޻k璆N7 gzۥ}nؗ-NvWMg3UTtj:Q5_%_%_ū_ū_ū_wVMwUMgOtj:Q5%L34LzF+{7{i0:,WuWa}871,uGKXO~To{wXPM; >rL25so9 l؈vz1 ðtbÏ?0l+T_Nۑ)gV#?ӗ{lxˣ*-OURlτĚ :2nLjH,RF'e)mnbTln>zJl=|hj/crd{++K{jibc-:^b u+Աݢcm:vXtlm:Mnױ[c:ӱش}LǞбtlձ:UC.X]ұS^ױOXQ":vM:t][٠ct,cQ zXeu,cu,c:бu,c#:ұ)K ۢc:U6;cuEceӱ{Sv:vc->Oǂ:KVn؀t!>3bmֱul Xt_؀-/_ѱ!{U&t5;cWu,cӱ{]u삎@i:J)h0ќ0Q絜7LK~\fQWVc=-BmS=-A97(Sꔻ#7973ԩs㦁E66B+'9džߔ;MxhSݹcN9s Tѩ&eҺ G*ܤӯjڪ{7Q'ƕݘubS9whT#ؑM{cz}wXS=۾O:wƇ .7vdPÉ=UDe;gϰs '6#N#Zh1-ƣd#chȗ4fK,KLD#{`ݑs#nICG/-^FJ뇎7̫P >^\-~qwTȝgkԡb{TằaqCGRMGLXHwG[ŭhqW;Z?^/ɍ?0.!<9#u#د@vme&d&d@>T=iɇVA#1=,=fC>-kWX+'3uv=#YqA|hf FCu_|$V,D=yq>Ԥ/R#3=votc+=dn>ˇjG_7L=Wgk'&cҍ´U Vta*6χ' bT VU*g bh>4U\yjh\ƿne]orEJץRrkRn- Ri,iKX*7m·ՒȚVf-\ZrǜjyP*smVˈT>>Zr\rB*ZfZHcr^*wn/5m_rnu^N)oJIy[J\;R!'OkP*)YRIʮ5.l*[WBdZ]V|VVuH* No}j*GCV5/B RWVTeZ/H>Y֗KV~%uRkj{C ŧtIy^oNS)9o-{;m0kfͯʅzUvVHdBO+dB=8u mɵ%~05eVP.467P\!ۗ]cZXX>9r:y\~8{:h 9WIޝ;p7wK׍4iO?RKlܰ8szYM׹e㦙wl\XX|>h M^&M '=zL7n2m~Ӝ]^ޜW[Ňf^ӟ7]ֹ>lfSO/7uQ3(^젱;4үa3%%|Xݪqߧn!zyŋ#p&Z?>~vMl=o>;>{yF#3TwyxtlWSr6h?%zϓS#zCs E՟o XfMFUnϷ/,tXXe鞅O] j(]{-Ӆ3gf~oy/ }Gle/z3^[Ls>`_h3O7/m >8vfP8kჇYz;Яȍ)yuvuNL#r= CNw11ciQc951ʤ3t,I wT2Yvvl*LtLw2ʨ9nxy3Kcɮ``}WgkLL2SOSTWb2cD4g+uu锷O'Rd|ҝ].eX<ΦRXBvwݥNoclɮt,uwwcjJ%2Lٺl&[t;wwO`}3N{Xg<Ofr(Ϧt6^jLVUϕLH:SXԳNyԳeSD:Z6:Sx"-?L&9 RD*N N)9Lz۰I~+N$u$.L ۥ)).̦Ki;RAoCS<љM]ݥIl[v|S"әɤ?xV%p5ӝxL6w4O2+$+GJ GeH_78 R*=nກ|8!K[?2훎70xGfçd>U5Slo_l򊚠i0[Н}`s#k&&1g_g?`g&zZFI+>wc v2No<8eX> 3XoԄABOenNL6˨k0|wZY=?X{)-|p+5ۺ9.].\x3ϼ~~OxzZ-:fjp=(ף\r=(ףnz^{yf_6GWmD\H_)UgWJ_w~x)ъmPgIi_b?Ŭ7pS^jʈ׽K~E!Xw.7ͷdlY&>^N멎up8V0s04c4