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G6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q+spacecurveF'/%'italicGQ&fa lseF'/%,mathvariantGQ'normalF'-I(mfencedGF$6$-F#67-F66&-F#6--F,6%Q\"tF 'F/F2-I#moGF$6-Q\"^F'F2/%&fenceGF1/%*separatorGF1/%)stretchyGF1/%*symm etricGF1/%(largeopGF1/%.movablelimitsGF1/%'accentGF1/%'lspaceGQ,0.1111 111emF'/%'rspaceGFU-I#mnGF$6$Q\"2F'F2-FB6-Q\",F'F2FE/FHQ%trueF'FIFKFMF OFQ/FTQ&0.0emF'/FWQ,0.3333333emF'F>FAFXFfnF>FA-FY6$Q\"3F'F2F2/%%openGQ \"[F'/%&closeGQ\"]F'FfnF>-FB6-Q\"=F'F2FEFGFIFKFMFOFQ/FTQ,0.2777778emF' /FWF\\p-FY6$Q\"0F'F2-FB6-Q#..F'F2FEFGFIFKFMFOFQ/FTQ,0.2222222emF'/FWF \\o-FY6$Q\"4F'F2-FB6-Q\"*F'F2FEFGFIFKFMFOFQ/FTQ,0.1666667emF'/FWF^q-F, 6%Q#PiF'F/F2Ffn-F,6%Q*linestyleF'F/F2Fho-F,6%Q&solidF'F/F2Ffn-F,6%Q&co lorF'F/F2Fho-F,6%Q%blueF'F/F2Ffn-F,6%Q%axesF'F/F2Fho-F,6%Q&BOXEDF'F/F2 F2-FB6-Q\";F'F2FEFinFIFKFMFOFQF[oF]p" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dr:=t->diff(r(t) ,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "v:=t->dr(t);" }}} {EXCHG 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t)*T(t)+kappa1(t)*(speed(t)^2)*N(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 44 "VIP: The coe fficients for T(t) and N(t) are " }{TEXT 212 17 "diffspeed(t) and " } {TEXT 212 36 "kappa1(t)*(speed(t)^2) respectively:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diffspeed(t);" }{MPLTEXT 1 0 22 "kappa1(t)* (speed(t)^2)" }{MPLTEXT 1 0 1 ";" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "acceleration1(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "acceleration2:=t->diff(v(t),t);" }{TEXT 217 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "acceleration2(t);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "evalm(subs(t=4,acceleration1 (t)));" }{TEXT 217 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "s ubs(t=4,acceleration2(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 217 10 "Ex ercise: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "r:=t->[t,(cos(t ))^2,(sin(t))^2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "dr:=t- >diff(r(t),t);" 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