{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Heading 2" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 2 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 9 "Calculo I" }}{PARA 256 "" 0 "" {TEXT -1 36 "Li\347\343o 17: O Teorema de Valor do Meio" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Recorde o Teormea de Rolle: " }}{PARA 0 "" 0 "" {TEXT -1 28 "Deixe f ser a fun\347\343o tal que" }}{PARA 0 "" 0 "" {TEXT -1 32 " 1) f \351 continua em [a,b] " }}{PARA 0 "" 0 "" {TEXT -1 33 " 2) f \351 diferente em (a,b) " }}{PARA 0 "" 0 "" {TEXT -1 23 " 3) f(a) = f(b). " }}{PARA 0 "" 0 "" {TEXT -1 52 "D epois, existe algum c em (a,b) tal que f '(c) = 0. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "1) Use o Teorema de Rolle para mostrar que " } {XPPEDIT 18 0 "3*x - 2 + cos( Pi*x/2" "6#,(*&\"\"$\"\"\"%\"xGF&F&\"\"# !\"\"-%$cosG6#*(%#PiGF&F'F&F(F)F&" }{TEXT -1 31 " tem exatamente uma r aiz real. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f1:= x -> 3*x - 2 + cos( Pi * x / 2);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,(*&\"\"$\"\"\"9$F/F/\" \"#!\"\"-%$cosG6#,$*&#F/F1F/*&%#PiGF/F0F/F/F/F/F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Vamos desenhar f1 para ver aonde as ra \355zes s\343o localizadas. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot(f1(x), x = -4 * Pi.. 4 * Pi, color = red);" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6#7S7$$!3+++#*eqjc7!#;$!3cL-;,I%p!RF*7$$! 3N[.^N[&=?\"F*$!3pKX%z%pg0PF*7$$!3Cn0%e6*=a6F*$!3+JY)37gte$F*7$$!3w,*p )GSe+6F*$!3fvS24Z$3]$F*7$$!3Aike7OiY5F*$!3'*[12c0B9MF*7$$!3ZQQU2m>H**! #<$!3Cl6`]69yKF*7$$!3kBd)zA#HJ%*FD$!3%4b$)*=-2#4$F*7$$!33_Z#G3Td\"*)FD $!3A/eIXBF*7$$!3ZERUmf(G#oFD$!39;k7*zFVF#F *7$$!3[iRPnoz!G'FD$!3#)G!*4*RoY<#F*7$$!3n79YR>\\OdFD$!3q*zIe!G]7?F*7$$ !3KWr;%G`>@&FD$!3aPZ:`yE'z\"F*7$$!3>7(eM$>iNZFD$!3E;ab!fT.e\"F*7$$!3Wh O*R*o$FD$!3/-L9Lu[=7F*7$$!3u[%f>Nc78 $FD$!3WVVoo\\!*=6F*7$$!3AiIW9_?PEFD$!3#*f\"\\&*Q9^/\"F*7$$!3q7Yp8G:&4# FD$!3U<)GTA4VF*FD7$$!3Ysa&Ru!**y:FD$!3=\")*z#)eah_(FD7$$!3)>bRJxH//\"F D$!39&\\H&yNv%=&FD7$$!3-[s!R\"oiea!#=$!3'z0NY&>@$)HFD7$$!3j+qiCf_S7!#> $!3jOGZEcSP5FD7$$\"3oul%)o22WGFir7$$\"3/,)*R%\\jS-\"F D$\"3I=G\"[j+W.\"FD7$$\"3XG?!*R;-X:FD$\"3K%>u&H3wz=FD7$$\"3iWq**zBA$3# FD$\"3g\"f0\\a*>eKFD7$$\"3AXxe/ou4EFD$\"3!z&)*)R\")4RD&FD7$$\"3^V2wei= >JFD$\"3++^?dVoVvFD7$$\"39g1d:>$[o$FD$\"3/g[qROVM**FD7$$\"37*G@jp*3$>% FD$\"3O[Tc=e26FL8F*7$$\"3/(\\BeM6^w&FD$\"35/)>A>jiV\"F*7$$\"3o.XRRd&4F'FD$ \"3ecRLw#3-f\"F*7$$\"3yGI6$))3(*z'FD$\"3WD*3$yu'*3=F*7$$\"3X4MPG " 0 "" {MPLTEXT 1 0 28 "fsolve(f1(x) = 0, x = 0..5);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Z2ncR!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Assim, aparece que a raiz real de f1 [e aproximadamente \+ " }{XPPEDIT 18 0 ".3956670747;" "6#-%&FloatG6$\"+Z2ncR!#5" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 63 "Como verificar nosso calculo num \351rico com o Teorema de Rolle ? " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 62 "Suponha o contr\341rio que f1 tem 2 ou ma is raiz real; disse a,b " }}{PARA 0 "" 0 "" {TEXT -1 45 "s\343o raiz r eal de f1, ex., f1(a) = f1(b) = 0. " }}{PARA 0 "" 0 "" {TEXT -1 66 "De pois pelo Teorema de Rolle l\341 existe algum c entre a e b, com " } }{PARA 0 "" 0 "" {TEXT -1 31 "f1 '(c) = 0. Mas f1 '(x) = 3 - " } {XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 9 " /2 sin( " }{XPPEDIT 18 0 " Pi;" "6#%#PiG" }{TEXT -1 21 " x/2 ) . Desde |sin( " }{XPPEDIT 18 0 "th eta;" "6#%&thetaG" }{TEXT -1 10 " )| < = 1 " }}{PARA 0 "" 0 "" {TEXT -1 10 "pata todo " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 18 " , n\363s temos que |" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 9 " /2 sin( " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 13 " x/2 )| < = " } {XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 9 " /2 < 3. " }}{PARA 0 "" 0 " " {TEXT -1 66 "Assim, f1 '(x) > 0 para todo x e assim n\363s temos uma contradi\347\343o. " }}{PARA 0 "" 0 "" {TEXT -1 41 "Logo, f1 tem prec isamente uma raiz real. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 63 "Vamos desenhar f1 '(x) para ver que realmente isto \351 > 0. 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7\"=Za&z%)=RF3$!3+<<$\\0'))f=F37$$\"3edXa()oGjXF3$!3H\")z([!4\"\\7#F37 $$\"3W%3**Hbm(H_F3$!39-xVO!G(zBF37$$\"37PRr4)3T*eF3$!3-T.WH'f;h#F37$$ \"3y\"[)yykYxlF3$!3*F3$!3OP=U7eFbLF37$$\"3#*R7\\HeV)y*F3$!3Co+yM(3VS$F37$$\"3#G[))* )3W'\\5!#<$!3L&f\"\\^.CCMF37$$\"30'[@XS@'46Fdp$!3T:M\"Rs&>2MF37$$\"3G9 w$3G*Qz6Fdp$!3q%3_[h&yYLF37$$\"3>%3*3tc9T7Fdp$!3'*e#Q[_EeD$F37$$\"3Ey0 DBA!*38Fdp$!3n(*R#4'>]9JF37$$\"3qjE.#[AMP\"Fdp$!3\"fdC7$ptQHF37$$\"3*R :_MgU2W\"Fdp$!3%f<$yhi$=r#F37$$\"3\"Qu#)**[jD]\"Fdp$!3)GKT,)H\"RY#F37$ $\"3=hw\"ymX#p:Fdp$!3E&y(>Q'fP:#F37$$\"3mwM!*4(4&Q;Fdp$!3#=*\\`(pMXy\" F37$$\"3CDL:iU!))p\"Fdp$!3BUiTY.;C9F37$$\"3o(R1/.CRw\"Fdp$!3z5*H!*HsY% **F-7$$\"32Id)H7*>J=Fdp$!3mG\\:=(y'o]F-7$$\"3Gfb7wY,(*=Fdp$\"3I4IsJXMY 7!#?7$$\"3cM5'zg%pg>Fdp$\"3\"fZ#few&*RbF-7$$\"3**oJ8:.SJ?Fdp$\"3s!*)\\ %H'f\"*>\"F37$$\"3)**p!zPD$\\4#Fdp$\"3u0tmyq4<=F37$$\"3k\"=$F37$$\"39/b=[33N P\"Fdp7$$\"3Kt2RXCLtIFdp$\"31MxQ6!f%o9Fdp7$$\"3!)***\\/l#fTJFdp$\"3O1_ 3Ajzq:Fdp-%+AXESLABELSG6$Q\"t6\"Q!F\\[l-%'COLOURG6&%$RGBG$\"*++++\"!\" )F(F(-%%VIEWG6$;F($\"+aEfTJ!\"*%(DEFAULTG" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "A partir do desenho, n\363s vemos que o objeto primeiram ente move para a esquerda e para a origem e depois continuamente move \+ para a direita. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "A Velocidade m\351dia do objeto no intervalo [0, " } {XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 14 "] \351 dada por: " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 " \+ ( s(" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 15 ") - s(0) ) / ( " } {XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 9 " - 0 ) . " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "A Velocidade instant \344nea no tempo c \351 dada por '(c). Assim, " }}{PARA 0 "" 0 "" {TEXT -1 37 "n\363s somos perguntados para resolver: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 " ( s(" } {XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 15 ") - s(0) ) / ( " } {XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 17 " - 0 ) = s '(c); " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "Precisame nte o MVT. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "s(Pi);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#!\"\"%#PiG\"\"\"F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "s(0);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "D(s);" } {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"tG6\"6$%)operat orG%&arrowGF&,&#\"\"\"\"\"#F,-%$cosG6#9$!\"\"F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "N\363s precisamos resolver: " }{XPPEDIT 18 0 "1 /2 = 1/2 - cos(t)" "6#/*&\"\"\"F%\"\"#!\"\",&*&F%F%F&F'F%-%$cosG6#%\"t GF'" }{TEXT -1 15 " para t em [0, " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" } {TEXT -1 34 " ], ex., n\363s queremos cos(t) = 0 " }}{PARA 0 "" 0 "" {TEXT -1 14 "para t em [0, " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 19 "]. A Solu\347\343o \351 t = " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" } {TEXT -1 50 " /2. Vamos desenhar a figura com a linha secante " }} {PARA 0 "" 0 "" {TEXT -1 27 "entre os pontos (0, 0) e ( " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" } {TEXT -1 39 " /2 ), e com a linha tangente para t = " }{XPPEDIT 18 0 " Pi;" "6#%#PiG" }{TEXT -1 6 " /2 . " }}{PARA 0 "" 0 "" {TEXT -1 31 "As \+ linhas podem ser paralelas. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "D(s)(Pi/2);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6## \"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "s(Pi/2);" } {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%!\"\"%#PiG\" \"\"F(F(F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots): " }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has be en redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "data:= ([ 0,0], [Pi, Pi/2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "a1:= \+ plot( [data], color=magenta, thickness=2 ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "a2:= plot(s(t), t = 0..5, color = green, thickness =2): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "a3:= plot((Pi/4 - \+ 1) + 1/2 * ( x - Pi/2), x = 0..Pi, color = magenta, thickness=2):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "a4:= textplot([1/5,1,`Secant Line`], align=\{RIGHT\}, color = blue, thickness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "a5:= textplot([1.5,-.8, `Tangent Li ne`], color = blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "dis play(\{a1,a2,a3,a4,a5\});" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CURVESG6%7$7$$\"\"!F)F(7$$\"37 $z*e`EfTJ!#<$\"3c'*[zEjzq:F--%'COLOURG6&%$RGBG$\"*++++\"!\")F(F4-%*THI CKNESSG6#\"\"#-F$6%7SF'7$$\"3GLLL3x&)*3\"!#=$!3zg$4m)fsFa!#>7$$\"3umm \"H2P\"Q?FA$!3#Hv`Q5()\\+\"FA7$$\"3MLL$eRwX5$FA$!3V!e)H-hl-:FA7$$\"33M L$3x%3yTFA$!3g)H?f\"=ao>FA7$$\"3emm\"z%4\\Y_FA$!3Ax)yuzZeQ#FA7$$\"3`LL eR-/PiFA$!3!R038\"y$>s#FA7$$\"3]***\\il'pisFA$!38.)z2>/&4IFA7$$\"3>MLe *)>VB$)FA$!36n]ED6RLKFA7$$\"3Y++DJbw!Q*FA$!3e[goZ!RQP$FA7$$\"3%ommTIOo /\"F-$!3\\R;#orlUU$FA7$$\"3YLL3_>jU6F-$!3!yM;SgMTQ$FA7$$\"37++]i^Z]7F- $!3]@QJ.w'*QKFA7$$\"33++](=h(e8F-$!3=9$Q$40C#)HFA7$$\"3/++]P[6j9F-$!3i 22W'H0li#FA7$$\"3UL$e*[z(yb\"F-$!3.uHQWex4AFA7$$\"3wmm;a/cq;F-$!3a$pe[ euuf\"FA7$$\"3%ommmJo;'*z*FD7$$\"3/+]iSj0x=F-$!3A)\\E@; lR\\\"FD7$$\"3gmmm\"pW`(>F-$\"3]\\qop*3#RoFD7$$\"3K+]i!f#=$3#F-$\"3ca% =3\">9+pxg#F-$\"37qTkx0c]zFA7$$\"33+]Pf4t.FF-$\"3Km'\\j A;'y#*FA7$$\"3uLLe*Gst!GF-$\"3s&[J5P`c2\"F-7$$\"30+++DRW9HF-$\"3n3x0\\ :-K7F-7$$\"3:++DJE>>IF-$\"39'z&\\#p,vQ\"F-7$$\"3F+]i!RU07$F-$\"3&fzAp[ A#R:F-7$$\"3+++v=S2LKF-$\"3dem4H3*yq\"F-7$$\"3Jmmm\"p)=MLF-$\"333O$>#> ]e=F-7$$\"3B++](=]@W$F-$\"3sT<%p)y7d.rvI#F-7$$\"3[m;H2qcZPF-$\"3dL,w#[Z%F-$\"3l'eE$zVK4KF-7$$\"3SnmT&G!e&e%F-$\"3a%er&)ogZG$F-7$$ \"3#RLLL)Qk%o%F-$\"3ee::rq$>M$F-7$$\"37+]iSjE!z%F-$\"3_C2+hA5#R$F-7$$ \"3a+]P40O\"*[F-$\"3=Kx$Qb2(HMF-7$$\"\"&F)$\"3cQJmuU#*eMF--F16&F3F(F4F (F7-F$6%7S7$F($!\"\"F)7$$\"3%)eD2LzxZoFD$!3'=PYL56wl*FA7$$\"3)\\$px*G* f!G\"FA$!33K:6b.qf$*FA7$$\"3+5@exGm]>FA$!3,X*37coY-*FA7$$\"3[99!=3o^i# FA$!3w#H*4ffT(o)FA7$$\"35!\\D0[nkH$FA$!3Sastfiw^$)FA7$$\"37\"=Za&z%)=R FA$!3))3kFAgdS!)FA7$$\"3edXa()oGjXFA$!3@@xAclN=xFA7$$\"3W%3**Hbm(H_FA$ !3yd/]Bn6&Q(FA7$$\"37PRr4)3T*eFA$!3+KI9&fXH0(FA7$$\"3y\"[)yykYxlFA$!3b edggnE6nFA7$$\"3[s'ocGo$zrFA$!3xjc;deJ5kFA7$$\"3UQ0;gr'p&yFA$!3MJ(>*>k ^rgFA7$$\"3vFMt?$[t`)FA$!3d&GL'ReKJdFA7$$\"3u\"p30k@I>*FA$!38acuz\"*[. aFA7$$\"3#*R7\\HeV)y*FA$!3/!Qa_3#y0^FA7$$\"3#G[))*)3W'\\5F-$!3'eed]bz< v%FA7$$\"30'[@XS@'46F-$!3upDRxH*=X%FA7$$\"3G9w$3G*Qz6F-$!3_G>\"ef`I5%F A7$$\"3>%3*3tc9T7F-$!3/zXbM;F%z$FA7$$\"3Ey0DBA!*38F-$!3s3ru$)))[bMFA7$ $\"3qjE.#[AMP\"F-$!3[\"oO)*e()G8$FA7$$\"3*R:_MgU2W\"F-$!3/I#RF)pG'z#FA 7$$\"3\"Qu#)**[jD]\"F-$!3)4G'3]D=([#FA7$$\"3=hw\"ymX#p:F-$!39%p64mrP:# FA7$$\"3mwM!*4(4&Q;F-$!3o;E[]9X2=FA7$$\"3CDL:iU!))p\"F-$!3vtLB*oyf]\"F A7$$\"3o(R1/.CRw\"F-$!3k6!oz%)z.=\"FA7$$\"32Id)H7*>J=F-$!3s'\\82&Q/S%) FD7$$\"3Gfb7wY,(*=F-$!3?N?s$>m#\\^FD7$$\"3cM5'zg%pg>F-$!3%=F[>gp_'>FD7 $$\"3**oJ8:.SJ?F-$\"3S\\%emv:+d\"FD7$$\"3)**p!zPD$\\4#F-$\"3Y**\\`*)oi YZFD7$$\"3k[Y'GY^w#FA7$$\"3z^r&[X%==EF-$\"3%*edGuA #44$FA7$$\"3'=BS\\0:[o#F-$\"3Nf6qu_2CMFA7$$\"3[gN,?R*3v#F-$\"3S-y1+'pW v$FA7$$\"3@/0LMNh6GF-$\"3-@Dlrw1eSFA7$$\"3w#oUX107)GF-$\"3&QT8FKDgS%FA 7$$\"3W46xe&[M%HF-$\"3BZb&QzUsr%FA7$$\"3H.6)e58)4IF-$\"3Y;bSHb1\\]FA7$ $\"3Kt2RXCLtIF-$\"3kmQ&pAimO&FA7$$\"3!)***\\/l#fTJF-$\"3,***\\ADjzq&FA F0F7-%%TEXTG6'7$$\"+++++?!#5$\"\"\"F)Q,Secant~Line6\"%+ALIGNRIGHTG-F16 &F3F(F(F4F7-Fc[m6%7$$\"#:Fa\\l$F6Fa\\lQ-Tangent~LineF\\\\mF^\\m-%+AXES LABELSG6%Q!F\\\\mFj\\m-%%FONTG6#%(DEFAULTG-%%VIEWG6$;F(Ff[lF^]m" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2 " "Curve 3" "Curve 4" "Curve 5" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "30 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }