0002000201000feActProject.ACT000102000aLimits.EAC0100000026c2  Limits.EACeActProject.ACT"&  I `E 'm[1bp\AuthorNnG|5Barry Kissane School of Education Murdoch University, WA, Australia kF@m2.edu.au http//wwwstaff. /~7 ʎ 1. Ob2}:To explore an importantcircular func l%from first principles.y *2. Example:[Consider the function[f(x)=,sin9xA . We willRexploreQisR forsvalues of x close to 0.\Tapsee graph -̈$( N&%FinaForm$NGraph2D% 3 LISTSYS$@4< Modify XP<STATCALC |d< \x Sequence,xSheetO | olveEq`wr(UptupFLG1 (<Lis{HDPicViewWind_osvev ̐xy^(!؈(U(E  P (  iT$0<HZST`lx !"̆# ؒ6C %&='| ,()*,  +< 8+D -P.\/h 0x(12$ 3Fu4<5H ETF`2lI,x J@ KT Lh MNOr̆ӆ Q-RÉ,S,, ]Pi ^d _x ` ab  ,͆ 8ΑD БP ב,\6ChّTt ڑh 9ۑ| FinancialFormaF $ system]^ 4_`ab( wLIST @L @xI<IS ab!Grapph2D37 ˈ p < -<]]  g(x)x 0+R"1!R) 0;-;0u[ 3. ExerciseExplore the limit of[ 1-cos Oas x approaches 0, in ansZlar way, using both?graphs and tables.p Solutions toampl̉ 7:Ls can be formally[evaluated from the 2D keyboard orMain:(using Calculatio menu). TL link belowqshows both methods.\Limit results -----ˈ'+ņR h() 0R1< lim((1-cosA )/,,0,0)3@3S Graph2D, 3@ LISTSYSL4NModify; ($< STATCALC U(< \< Sequence<,xSheet4|olveEqLwr0 (Up< tupFLG1H<(<Lis{pdDPic ViewWind؆,@x ( <P$dx <  HT`lx !"̒#ؒ$%&'@(T)h*|,+8D-P  .\0h1t2345EFHȒIԒJKLM,N@OT^k(Q|R@STX ]d ^h_l`patbx|͒2ΒВ! system( ]LIST @LIST @@xLISTL @@xSTLI @@xTLIS = abIGrapph2D[_ system]^  <(10qy`H#YuYU 0 H$H5a  `$ Oq[;eAct FH$x^(f(a(x,1)))GH$x^(g(a(x,1))) angles  $0<HT`lx @`u8area D $0<HT`lxY5Ya`HyTe`aI(X6fGH 3U2F`7sC)E(8xGEaRB'HgC63@TGQC'S8sP06C 62)GU2AX7 T X6b3SfH(x((x^(3)-1)/((x)-1))gH x((L(x))/(x))m_angle m_area volume D $0<HT`lxY5Ya`HyTe`aI(X6fGH 3U2F`7sC)E(8xGEaRB'HgC63@TGQC'S8sP06C 62)GU2AX7 T X6b3Sx D $0<HT`lx        ( 2 < P d x   xyyy 010008main.ACT0001020012eActivity Save.EAC0100000026c2  Limits.EACeActProject.ACT"&  I `E 'm[1bp\AuthorNnG|5Barry Kissane School of Education Murdoch University, WA, Australia kF@m2.edu.au http//wwwstaff. /~7 ʎ 1. Ob2}:To explore an importantcircular func l%from first principles.y *2. Example:[Consider the function[f(x)=,sin9xA . We willRexploreQisR forsvalues of x close to 0.\Tapsee graph -̈$( N&%FinaForm$NGraph2D% 3 LISTSYS$@4< Modify XP<STATCALC |d< \x Sequence,xSheetO | olveEq`wr(UptupFLG1 (<Lis{HDPicViewWind_osvev ̐xy^(!؈(U(E  P (  iT$0<HZST`lx !"̆# ؒ6C %&='| ,()*,  +< 8+D -P.\/h 0x(12$ 3Fu4<5H ETF`2lI,x J@ KT Lh MNOr̆ӆ Q-RÉ,S,, ]Pi ^d _x ` ab  ,͆ 8ΑD БP ב,\6ChّTt ڑh 9ۑ| FinancialFormaF $ system]^ 4_`ab( wLIST @L @xI<IS ab!Grapph2D37 ˈ p < -<]]  g(x)x 0+R"1!R) 0;-;0u[ 3. ExerciseExplore the limit of[ 1-cos Oas x approaches 0, in ansZlar way, using both?graphs and tables.p Solutions toampl̉ 7:Ls can be formally[evaluated from the 2D keyboard orMain:(using Calculatio menu). TL link belowqshows both methods.\Limit results -----ˈ'+ņR h() 0R1< lim((1-cosA )/,,0,0)3@3S Graph2D, 3@ LISTSYSL4NModify; ($< STATCALC U(< \< Sequence<,xSheet4|olveEqLwr0 (Up< tupFLG1H<(<Lis{pdDPic ViewWind؆,@x ( <P$dx <  HT`lx !"̒#ؒ$%&'@(T)h*|,+8D-P  .\0h1t2345EFHȒIԒJKLM,N@OT^k(Q|R@STX ]d ^h_l`patbx|͒2ΒВ! system( ]LIST @LIST @@xLISTL @@xSTLI @@xTLIS = abIGrapph2D[_ system]^  <(10qy`H#YuYU 0 H$H5a  `$ Oq[;eAct FH$x^(f(a(x,1)))GH$x^(g(a(x,1))) angles  $0<HT`lx @`u8area D $0<HT`lxY5Ya`HyTe`aI(X6fGH 3U2F`7sC)E(8xGEaRB'HgC63@TGQC'S8sP06C 62)GU2AX7 T X6b3SfH(x((x^(3)-1)/((x)-1))gH x((L(x))/(x))m_angle m_area volume D $0<HT`lxY5Ya`HyTe`aI(X6fGH 3U2F`7sC)E(8xGEaRB'HgC63@TGQC'S8sP06C 62)GU2AX7 T X6b3Sx D $0<HT`lx        ( 2 < P d x   xyyy 03010a00200008000000001ba4x}l[}{(hINܖIXovMx&o"۲%7ɖҖ %E/͹֥TU;#06` 6a03,67lM[y1tEa]߹%m~?^KudYN5F\~p|P5qrbra>8m^u_>ZxjW ѱXm ޶:X5X5X5zбuKѱ>۠c) 'ulZ>cgt,c9W.}:vYױekԱ:]ӱu{H:б[:֤c?ұObB:Qb:Աmұ=ctYvXX=cm:6c:6c[t촎ұֱ%ұK:W^ӱֱأ:u:On~{W{:St젎Eu쐎mб^KXS:)1i۩cXt[:֣cGtOtqݗ/X}St-;cu,cұ{G.طuUi:z! 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