00020001010008main.ACT000202000cImp_Diff.EAC01000000244c  [[-3],[-2]]# #`gu#`gu   5x^2-5y^2-25=0     $&@hq'GF8x^2+18y^2-144=0   @623xYTp"R 8gPIc` y=1.5x+2.5 %`@6Tq) 2tS 2IAXy=-0.6667x-4bVVxX `59RC@`0: <vKr  A 'L'pC uxy qq   `0677Fϖ (GOW_gE  final.EAC main.ACT&)-@ ~E 'N[4Implicit Differentiation \( Author?CProfessor Wei-Chi Yang Radford University 9e-l: wy0@r).edu""URL: http://www.$/6f Sound Track"Professor Jonathan Lewin Kennesaw Sate University A e-mail: l6s@mindspring.comFURL: http://www.mj-movies'[ Objectns:[7S1. We will use ClassPad (CP) to explore the graphs of implicit equationd its corresponding deriva}.|T2|b one problem 4t c8be fouYn regular Calculus texbookszwe1CPis\extendresult., [ Note. 1L We will explore some implicit equations that a!graphabl8thin ClassPad.[Ti ExaIe 1n= WFiNI of derivkve (dy/dx) for x^2-y5=0_HStep[ drag and drop] intoo following Ge try Strip.\ DEzΈy}JORH `@Gs# . ! DvKr  A L C uxy   JH  N\Dsf `  FT'@7`Xp$i!22`030%YDiPT2Yt<upQH "ix$d` eTcb`57b0 F y $<Tl,D Ds f5PgD qds0,2xp8yu)`DhQG"@PDIH`S0`T #gvl`t`IH`p  VT`TR` SxY $- N&%FinaForm$NGraph2D% 3 LISTSYS$@4< Modify XP<STATCALC |d< \x Sequence,xSheetO | olveEq`wr(UptupFLG1 (<Lis{HDPicViewWind_osvev(̐xy^ Uy2(h<hP 0)  jxy[O!PWe use the following m1 to denotslop!r)tangent line of C1 at (a,b).ym1:zab4*+9*72-49222-49 -4a 9b[ /4Step 2. We find the intersections between C1 a!C2.RRL +solve({x^2-y5=0,4*+9*72=0},{x,y})R x=-3,y=-2,x=4332[TM3show slopes of mm2 at (-2) resp vely are nega @!ciprocalEeach o9r.  m1|a|b=-23.2.-23[<:Step 4. We find the tangent lines at (-3,-2) respectively:RQWy=-2+(3/2)*(x+3)Ry= 3(-2TT-2/3U-2V^V[65creategeometryks forpoiof -ea , C1: x^2-y5=02: wB74*x^2+9*y^2-72=0 and the respective tangent lines of C1'C2 at -3 2, y=!3,x+-25-2 I8-29n- s follows:[-A poiinterson:]&-Equaellipse" "" hyperbola$$;F@5rU=9aH9!-Equation of the tangent line forellipse at a point:][3Step 6. We dragIm intoSgeometry strip below:\;?Measurxhoatw3 s=>IndeedSAay perpendicularΈ[ Explor:K Go(above) =>Edit=>Select all=> D sitems Taround and notic@DeTsV4dk va accordingly.˖erci1.{4Repeat the process for showingtangent lines -3-2,!-"! andE#a)C11C2 respectively arerpendicular.[[W Exercise 2.NIFollowStep 6 m ioned aboveexploreExcFsee if X#A^ intersons stay when youperform horizontal or vertic shiftings.eActm1(( bam2@@  basecH t1/P(t)020012eActivity Save.EAC01000000244e  [[-3],[-2]]# #`gu#`gu   5x^2-5y^2-25=0     $&@hq'GF8x^2+18y^2-144=0   @623xYTp"R 8gPIc` y=1.5x+2.5 %`@6Tq) 2tS 2IAXy=-0.6667x-4bVVxX `59RC@`0: <vKr  A 'L'pC uxy qq   `0677Fϖ (GOW_gE  Imp_Diff.EAC main.ACT),0C ~E 'N[4]licit b erentiation \( Author?CProfessor Wei-Chi Yang Radford University 9e-l: wy0@r).edu""URL: http://www.$/6f Sound Track"Professor Jonathan Lewin Kennesaw Sate University A e-mail: l6s@mindspring.comFURL: http://www.mj-movies'[ Objectns:[7S1. We will use ClassPad (CP) to explore the graphs of implicit equationd its corresponding deriva}.|T2|b one problem 4t c8be fouYn regular Calculus texbookszwe1CPis\extendresult., [ Note. 1L We will explore some implicit equations that a!graphabl8thin ClassPad.[Ti ExaIe 1n= WFiNI of derivkve (dy/dx) for x^2-y5=0_HStep[ drag and drop] intoo following Ge try Strip.\ DEzΈy}JORH `@Gs# . ! DvKr  A L C uxy   JH  N\Dsf `  FT'@7`Xp$i!22`030%YDiPT2Yt<upQH "ix$d` eTcb`57b0 F y $<Tl,D Ds f5PgD qds0,2xp8yu)`DhQG"@PDIH`S0`T #gvl`t`IH`p  VT`TR` SxY $- N&%FinaForm$NGraph2D% 3 LISTSYS$@4< Modify XP<STATCALC |d< \x Sequence,xSheetO | olveEq`wr(UptupFLG1 (<Lis{HDPicViewWind_osvev(̐xy^ Uy2(h<hP 0)  jxy[O!PWe use the following m1 to denotslop!r)tangent line of C1 at (a,b).ym1:zab4*+9*72-49222-49 -4a 9b[ /4Step 2. We find the intersections between C1 a!C2.RRL +solve({x^2-y5=0,4*+9*72=0},{x,y})R x=-3,y=-2,x=4332[TM3show slopes of mm2 at (-2) resp vely are nega @!ciprocalEeach o9r.  m1|a|b=-23.2.-23[<:Step 4. We find the tangent lines at (-3,-2) respectively:RQWy=-2+(3/2)*(x+3)Ry= 3(-2TT-2/3U-2V^V[65creategeometryks forpoiof -ea , C1: x^2-y5=02: wB74*x^2+9*y^2-72=0 and the respective tangent lines of C1'C2 at -3 2, y=!3,x+-25-2 I8-29n- s follows:[-A poiinterson:]&-Equaellipse" "" hyperbola$$;F@5rU=9aH9!-Equation of the tangent line forellipse at a point:][3Step 6. 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