**TI89**09/26/02, 09:04 booktandemolimdemoDseriescrsumsbetween*eulertb+eulergrL,mfield-2Zoff-grid-zz0a1a/off-grid-f3g0a1a/on-grid-f3f0a1a/,f3e0a1a/*f3d0a1a/)f3c0a1a/"f3b0a1a/res.scy+mxy*mny)scx(mxx'xm& resxres-Cscyyscl-Cmxyymax-Cmnyymin-Cscxxscl-Cmxxxmax-Cxmxmin-CWindow-Vf3a0top/ derstbCurrent derivative is: -Vf2b0top/ eqstbCurrent equation is: -Vf1b0top/derst- derstEnter new f'(x)= -CCurrent f'(x) is -derstbGuess f'(x) -VQf2a0Qy1-Oxay1mxastepxastepxay1mxastepxastepxQmxaypixxaGmxaypixxaGmxaxaxpixGmxaxaxpixGmxaxaGxay1mxastepxastepxay1mxastepxastepxxay1Łmxaxastepxa2txastepxaff10zzQuit-Vf3gGrid off-Wf3fGrid on-Wf3eZoom Trig-Wf3dZoom Standard-Wf3cZoom Square-Wf3bZoom Decimal-Wf3aWindow Editor-WSet window-Vff1Push ENTER to draw-WDraw tangents-V &stepxa'&xpix*)fypix'&2stepa1a0thick-Aeqsty1چ eqstEnter f(x)= -CCurrent f(x) is -eqstbEnter new f(x)-Vf1a0zzQuit-Vf3fGrid off-Wf3fGrid on-Wf3eZoom Trig-Wf3dZoom Standard-Wf3cZoom Square-Wf3bZoom Decimal-Wf3aWindow Editor-WSet window-Vf2bView last guess-Wf2aGuess y'(x) = -WDerivative-Vf1bCurrent equation-Wf1aNew Equation-WEquation-Vtop0f1a/{RADIAN-Angle-none-derstnone-eqstdersteqstm|(C) COPYRIGHT, LIN McMULLIN, 1994, 1995,1999, 2001 VERSION 3-m50tools/ON-Pretty Print-Float-Display Digits-aay1 Mf(x) = - M MBottom = -M MBox Top = -Maa MRight = -Maa MBox Left = -MM =-MM =-MFix 8-Display Digits- Mf(x) ==> -Maa MAs x ==> -MOFF-Pretty Print-m40tools/y1-dr20tools/aaaaxaaaaxaaaaxaaaaxaaFysaaxsysaaxsxysaaxsysaaxsx*)?ys'&~xssq20){sq10@#*@#)aa@#'aa@#&m30tools/curdelcurlimcurepicurxaaeqsty1چ curdelDelta, (e) =-CcurepiEpsilon =-Ccurlimf(x) approaches-CcurxAs x approaches-Ceqstf(x) = -C LIMIT -Vm20m5 QUIT -Vm4 Data -Vdr2 Graph f(x) -Vm3 Box -Vm2 Limit -Vtools0-zeqsty1چ.01-curepie/4-curdel9-curlim2-curx4x+1-eqst{AUTO-Exact/Approx-zz0s1a/ps ڋpspspptools/z psppK;s1b0tools/ psK;tools/;Push F4 to stop.-<Mps-M --Mis--Mstr1MPartial Sum of - MMn = -Ms1a0pppsstr1 ڀstr5 str5Start n at n = -Cstr1a(n) = -CEnter Sequence as function of n-Vs10s2a/tools/;ahszahshshstools/;Push F4 to stop.-<Mahs-MAlternating Harmonic Series = -"MhsMHarmonic Series = - MMn = -Ms2a0ahshss20zzExit-Vs2Harmonic Series-Vs1Enter sequence-Vtools0FLOAT 12-Display Digits-APPROXIMATE-Exact/Approx-.L 8(C) COPYRIGHT Version 2.0 LIN McMULLIN, 1994, 1997, 1999, 2002-cldrwzz0cc/ON-Pretty Print- y1K@MEXACT = -BMfloattrsttlstK7MTRAP RULE = -7MmxmnstK,MMAX ERROR = -,MmxmnK!MMAX - MIN = -!MfixstKMDELTA = -MtrstK MRIGHT SUM =- MtlstKMLEFT SUM = -MOFF-Pretty Print-floatvals10cc/AUTO-Exact/Approx-ON-Pretty Print- y1K@MEXACT = -BMfloattrsttlstK7MTRAP RULE = -7MmxmnstK,MMAX ERROR = -,MmxmnK!MMAX - MIN = -!MfixstKMDELTA = -MtrstK MRIGHT SUM =- MtlstKMLEFT SUM = -MAPPROXIMATE-Exact/Approx-OFF-Pretty Print-floatvals0aa/cg0cc/y1ڍtll30\y1ڋ xy1 x  stxsty1 =l20y1y1  x  recst left10cc/trr30r2/ :y1ڋy1xy1  recy1 recxy1y1stxy1st stxsty1 r20y1  x  recstr10mx  recmx recxmn  recmn recxmx  recmn  recxmx recmn recx right10zzQuit-Vvals1Data (exact)-WvalsData (approximate)-W Data -Vaa1Change interval-WaaChange function-W Changes -VcgClear graph-Wright1RIGHT SUM-Wleft1LEFT SUM-W RIEMANN SUMS -V ob oacc0BEFORE using VALUE-MDo BOTH LEFT & RIGHT-M'&V (  rec'*)V + ?# ' ?# &)z)***mx)mnyyy))**yyy)*; y1* y1) ' &SCALE-cc/ ob oa:rectrecrght lft rectNumber of rectangles-CrghtRight endpoint b = -ClftLeft endpoint a = -CInterval-Vaa10srt1y1ڀ srt1f(x) =-Cf(x) should be monotone.-bLeft & Right Sums for f(x) on [A,B]-Vaa0cllcdFUNCTION-Graph-cldrw?#ob?#oaVERSION 2.0-7 cldrwbzz0start/Version 1.0 April 24,2000-z Lin McMullin, 2000-zabout0start/toolbars, or use then now.-program and use the -equations.Then run the -program and enter the-y1(x) and y2(x),EXIT the-To find the area between-zdir0start/auto-Exact/Approx-ON-Pretty Print-rec<MR = -x<M P<Mb = -<<M <Ma = -<Mexact-Exact/Approx- y1y2ڍKK0MEXACT = -0MfloatstK$MDELTA = -$MltotrtotstKM(L + R)/2 =-MrtotstK MRIGHT SUM =- MltotstKMLEFT SUM = -MOFF-Pretty Print-floatbvals10start/AUTO-Exact/Approx-ON-Pretty Print-rec<MR = -x<M P<Mb = -<<M <Ma = -<Mexact-Exact/Approx- y1y2ڍKK0MEXACT = -0MfloatstK$MDELTA = -$MltotrtotstKM(L + R)/2 =-MrtotstK MRIGHT SUM =- MltotstKMLEFT SUM = -MAPPROXIMATE-Exact/Approx-OFF-Pretty Print-floatbvals0start/bcg0start/bl30sty1y2ڍKltotltoty1y1stxy1sty2stxy2sty2xy2y1x =bl20ltot  recst bleft10start/bl30y1y2ڍKrtotrtoty1y1stxy1sty2stxy2sty2xy2y1xst =bl20rtot  recst bright10start/ ob oabcc0BEFORE using VALUE-MDo BOTH LEFT & RIGHT-M'&V (:b+3*(b-a)/recxmax-*)V + ?# ' ?# &)z)***mx)mn'? #''&? #&&# ' &SCALE-start/ ob oa:recSNumber of rectangles-z auto-exact/approx-ON-Pretty Print-recP$MRectangles = -$M Mb = -M  Ma = - MCurrent values:-Mexact-exact/approx-OFF-Pretty Print-baa0Q -zfor area between y1(x) and y2 on (a,b).-zLeft and Right Sums-zcllcdFUNCTION-Graph-cldrw?#ob?#oabetween0bzz EXIT -VaboutAbout-WdirDirections-Wbvals1Data (exact)-WbvalsData (approximate)-Wbaa[a,b], rectangles-W Start & Data -VbcgClear graph-Wbright1RIGHT SUM for Area-Wbleft1LEFT SUM for Area -W RIEMANN SUMS -Vstart0'end /Q y1slope = -zy(x(n)) = -zx(n) = -z y1ڏ 0STEP SIZE-S Y(x)= -SINITIAL x= -S{ܤT() Prgm :ClrIO Input "INITIAL x= ",x :Input "Y(x)= ",y :Input "STEP SIZE",h :Lbl pp :x+hu :y+h*y1(x)v :Line x,y,u,v ux vy If xxmax Then Goto pp EndIf EndPrgmܥ3zz0a1a/off-grid-f3g0a1a/on-grid-f3f0a1a/,f3e0a1a/*f3d0a1a/)f3c0a1a/"f3b0a1a/res.resxres-C. resscy+scyyscl-C+ scymxy*mxyymax-C* mxymny)mnyymin-C) mnyscx(scxxscl-C( scxmxx'mxxxmax-C' mxxxm&xmxmin-C& xmf3a0tools/pp/';  x y1ڏpp0str4str3 str2 str4STEP SIZE-Cstr3Y(x)= -Cstr2INITIAL x= -CInitial Conditions-Veg0tools// =/=   x   Q y10 0)?P# &?P#?@# ?@# *)7'&S{cldrwsf0tools/str1y1ڀ  str1dy/dx = -CEnter dy/dx-Venter0zzExit-Vf3fGrid off-Wf3fGrid on-Wf3eZoom Trig-Wf3dZoom Standard-Wf3cZoom Square-Wf3bZoom Decimal-Wf3aWindow Editor-WWindow-VegEulerGraph-VsfSlopeField-Venterdy/dx=-Vtools0a1a0{cldrw