{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title " 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 27 "Aplikace integralniho poc tu" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Delka krivky." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "k:=ln(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG-%#lnG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(ln(x), x=sqrt(3)..sqrt(15));" }}{PARA 13 "" 1 " " {INLPLOT "6%-%'CURVESG6$7S7$$\"1++V330K=F*$\"1]N_GSj%)fF-7$$\"14ou!e%) \\'=F*$\"1/_l`y_KiF-7$$\"1%\\(*3w]4\">F*$\"18\\\"y)*3gZ'F-7$$\"1(p<=Z) pc>F*$\"1Q\"=!)*fe7nF-7$$\"1X`&fX7\"**>F*$\"1KnT+J.FpF-7$$\"1Sg\")z'HI /#F*$\"1dK&HVQV9(F-7$$\"13qbN*[%)3#F*$\"1vFgVl@ktF-7$$\"1!zo6`AP8#F*$ \"1^PV:7oyvF-7$$\"1$y(3*)>H!=#F*$\"1!o.y2)e%z(F-7$$\"1;6(HR58A#F*$\"1' *=\\))G(4)zF-7$$\"177c+u[nAF*$\"1ViekMs'=)F-7$$\"1p5Q:S&QJ#F*$\"13=>#R X\"*Q)F-7$$\"1,[GSo`eBF*$\"1'f%QQWT!e)F-7$$\"1;&))f78\"*R#F*$\"1nVA#Q \"*4v)F-7$$\"18EJaAOZCF*$\"1@Y!o83,&*)F-7$$\"1/<&[fN#)[#F*$\"1eReG'Qd6 *F-7$$\"1m(zm+\"yNDF*$\"1GP8!z;]I*F-7$$\"1+wS_n'yd#F*$\"10dgn@ip%*F-7$ $\"10Hq&[TSi#F*$\"1m0d5o:Z'*F-7$$\"1pK<^2,oEF*$\"1lR?x:L8)*F-7$$\"1]F, n!))Qr#F*$\"1R$=vv*)GF* $\"1_*y!f1pUV(HT$HF*$\"1dmS**3Tw5F*7$$\"1ZF,tj(*zHF*$\"1qm '>P:>4\"F*7$$\"1,Bnb$G[-$F*$\"14k%zMao5\"F*7$$\"1+99b\\AoIF*$\"1G[(Q?* 4@6F*7$$\"1sT$*z%4k6$F*$\"1A.UJ:oO6F*7$$\"1%z`&=aqfJF*$\"1NnF,)y/:\"F* 7$$\"1,LOuI$f?$F*$\"1c)[)yJ+l6F*7$$\"1>tI,A#yC$F*$\"1zU#)zY)z<\"F*7$$ \"1paU\"3=OH$F*$\"1U`K\"o')>>\"F*7$$\"1`-mN%3nL$F*$\"1k0wA[)\\?\"F*7$$ \"15ovr-v\"Q$F*$\"1!)pM2MR=7F*7$$\"1x#R%**oyDMF*$\"1?k)p>J8B\"F*7$$\"1 v0_n\"*)=Z$F*$\"1B:\\u))pW7F*7$$\"1*Rn58\"H;NF*$\"1*ex\"ynSd7F*7$$\"1@ <\">b)phNF*$\"1p7S_vBq7F*7$$\"1RdQw*Hng$F*$\"14F7Q:!GG\"F*7$$\"1OXpy\" 4\"[OF*$\"1`W8+!4UH\"F*7$$\"1.5=9W`&p$F*$\"10alv^728F*7$$\"1O/;5@&zt$F *$\"1I-L(*y`=8F*7$$\"1cmA@#yJy$F*$\"17TibWcI8F*7$$\"1r(Q-Qlk#QF*$\"1Jp &)*\\T>M\"F*7$$\"1++FWL)H(QF*$\"1m30+^-a8F*-%'COLOURG6&%$RGBG$\"#5!\" \"\"\"!F_[l-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;$\"+330K " 0 "" {MPLTEXT 1 0 15 "diff(ln(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$%\"xG !\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(%, x=sqrt(3). .sqrt(15));" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7S7$$\"1++V330 K= F*$\"1alGneb'\\&F-7$$\"14ou!e%)\\'=F*$\"1nF3EY(>O&F-7$$\"1%\\(*3w]4\"> F*$\"1+G))4s*HB&F-7$$\"1(p<=Z)pc>F*$\"1G'RfY\\16&F-7$$\"1X`&fX7\"**>F* $\"1Qo@X)>A+&F-7$$\"1Sg\")z'HI/#F*$\"1cI1'\\\"p%*[F-7$$\"13qbN*[%)3#F* $\"1&HLG_U#)y%F-7$$\"1!zo6`AP8#F*$\"1k2'\\)\\k'o%F-7$$\"1$y(3*)>H!=#F* $\"1(H^@kTle%F-7$$\"1;6(HR58A#F*$\"1Qu=7s%=]%F-7$$\"177c+u[nAF*$\"1L/^$F-7$$\"1nnCC>v*)GF*$\"1Ha'*fY]gMF-7$$\"1>pUV(HT$HF*$\"1[$ 3/el\"3MF-7$$\"1ZF,tj(*zHF*$\"1$pmRIJdN$F-7$$\"1,Bnb$G[-$F*$\"1uvA6F(f I$F-7$$\"1+99b\\AoIF*$\"1D&*\\OM@fKF-7$$\"1sT$*z%4k6$F*$\"1p!=5%4#)3KF -7$$\"1%z`&=aqfJF*$\"1gTy&*>&[;$F-7$$\"1,LOuI$f?$F*$\"1bAz/n@>JF-7$$\" 1>tI,A#yC$F*$\"1Snq!G')*yIF-7$$\"1paU\"3=OH$F*$\"1@4JLZHF-7$$\"1v0_n\"*)=Z$F*$\"1-?RviF!)GF-7$$\"1*Rn58\"H;NF* $\"16\\%*)e0R%GF-7$$\"1@<\">b)phNF*$\"18Zvu\"\\w!GF-7$$\"1RdQw*Hng$F*$ \"19@U%e%fsFF-7$$\"1OXpy\"4\"[OF*$\"1\"=U@.Y6u#F-7$$\"1.5=9W`&p$F*$\"1 56+x&ofq#F-7$$\"1O/;5@&zt$F*$\"1&Gn(o;EvEF-7$$\"1cmA@#yJy$F*$\"1v(oue#F --%'COLOURG6&%$RGBG$\"#5!\"\"\"\"!F_[l-%+AXESLABELSG6$Q\"x6\"%!G-%%VIE WG6$;$\"+330K " 0 "" {MPLTEXT 1 0 51 "l:=Int(sqrt(1+(Diff(k,x))^2), x=sqr t(3)..sqrt(15));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG-%$IntG6$*$- %%sqrtG6#,&\"\"\"F-*$)-%%DiffG6$-%#lnG6#%\"xGF6\"\"#\"\"\"F-F8/F6;*$-F *6#\"\"$F8*$-F*6#\"#:F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " l:=Int(sqrt(1+(diff(k,x))^2), x=sqrt(3)..sqrt(15));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"lG-%$IntG6$*$-%%sqrtG6#,&\"\"\"F-*&\"\"\"F/*$)%\" xG\"\"#F/!\"\"F-F//F2;*$-F*6#\"\"$F/*$-F*6#\"#:F/" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "simplify(changevar(x^2+1=t^2, l, t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&*&-%%sqrtG6#*&*$)%\"tG\"\"#\"\"\"F0,&! \"\"\"\"\"*$F-F0F3!\"\"F0F.F3F0*$-F)6#F1F0F5/F.;F/\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"#\"\"\"-%#lnG6#\"\"$F%-F'6#\"\"&#!\"\"F$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Urcete delku kruznice o polomeru r =1. 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{MPLTEXT 1 0 29 "v:=Pi*Int(f(x)^2, x=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG*&%#PiG\"\"\"-%$IntG6$,$*$)-%$absG6#-%$sinG6 #%\"xG\"\"#\"\"\"\"\"%/F4;\"\"!,$F&F5F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$)%#Pi G\"\"#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "s:=2*P i*Int(f(x)*sqrt(1+(Diff(f(x), x))^2), x=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG,$*&%#PiG\"\"\"-%$IntG6$,$*&-%$absG6#-%$sinG6#%\" xGF(-%%sqrtG6#,&F(F(*$)-%%DiffG6$,$F.\"\"#F4F?\"\"\"F(F@F?/F4;\"\"!,$F 'F?F(F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(value(s)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%#PiG\"\"\"-%%sqrtG6#\"\"&\" \"\"\"\")*&F%F+-%#lnG6#,&\"\"#F&*$F'F+F&F&\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Objem a povrch koule o polomeru r>0." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(r>0);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "f:=x->sqrt(r^2-x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(-%%sqrtG6#,&*$) %\"rG\"\"#\"\"\"\"\"\"*$)9$F3F4!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "v:=Pi*Int((f(x))^2, x=-r..r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG*&%#PiG\"\"\"-%$IntG6$,&*$)%#r|irG\"\"#\"\"\"F'*$ )%\"xGF/F0!\"\"/F3;,$F.F4F.F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%#PiG\"\"\")%#r| irG\"\"$\"\"\"#\"\"%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "s :=2*Pi*Int(f(x)*sqrt(1+(Diff(f(x), x))^2), x=-r..r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG,$*&%#PiG\"\"\"-%$IntG6$*&-%%sqrtG6#,&*$)%#r|i rG\"\"#\"\"\"F(*$)%\"xGF4F5!\"\"F5-F.6#,&F(F(*$)-%%DiffG6$*$F-F5F8F4F5 F(F5/F8;,$F3F9F3F(F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "valu e(s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%#PiG\"\"\")%#r|irG\"\"# \"\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Urcete objem koule (rotaci krivky dane parametricky)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "x=r*cos(t), y=r*sin(t)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "V:=2*Pi*Int(Diff(r*sin(t),t)^2*abs(Diff(r*cos(t), t)), t=0..Pi); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG,$*&%#PiG\"\"\"-%$IntG6$*&)- %%DiffG6$*&%#r|irGF(-%$sinG6#%\"tGF(F6\"\"#\"\"\"-%$absG6#-F/6$*&F2F8- %$cosGF5F(F6F(/F6;\"\"!F'F(F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%#PiG\"\"\")%#r| irG\"\"$\"\"\"#\"\"%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "39 0 0" 7 }{VIEWOPTS 1 1 0 1 1 1803 }