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0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 406 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 407 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 408 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 409 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 410 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 411 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 412 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 413 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 414 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 415 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 416 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 417 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 418 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 419 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 420 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 421 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 422 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 423 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 424 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 425 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 426 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 427 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 428 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 429 1 {CSTYLE "" -1 -1 "" 1 18 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 "" 0 430 1 {CSTYLE "" -1 -1 "" 1 18 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 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 29 "MATEMATICKA ANALYZA V MAP LU \n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 "Symbolicke derivovani" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 331 "" 0 "" {TEXT -1 56 "Pomoci procedury diff muzeme derivovat formul e (vyrazy):" }}{PARA 258 "> " 0 "" {MPLTEXT 1 0 20 "'diff(exp(-x^2),x) ';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%diffG6$-%$expG6#,$*$)%\"xG\" \"#\"\"\"!\"\"F," }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 181 "Apostrofy \+ kolem predchazejiciho prikazu zamezi vyhodnoceni.\nStejneho efektu dos ahneme i procedurou Diff. Diff se pouziva pro vetsi prehlednost a z du vodu\nkontroly spravnosti zadani." }}{PARA 260 "> " 0 "" {MPLTEXT 1 0 2 "%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"xG\"\"\"-%$expG6#,$*$) F%\"\"#\"\"\"!\"\"F&!\"#" }}}{EXCHG {PARA 261 "> " 0 "" {MPLTEXT 1 0 44 "Diff(ln(x/(x^2+1)),x)=diff(ln(x/(x^2+1)),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%#lnG6#*&%\"xG\"\"\",&*$)F+\"\"#F,\"\"\"F1F 1!\"\"F+*&*&,&*&F,F,F-F2F1*&*$F/F,F,*$)F-\"\"#F,F2!\"#F1F-F1F,F+F2" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Diff(ln(x/(x^2+1)),x):%=val ue(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%#lnG6#*&%\"xG\" \"\",&*$)F+\"\"#F,\"\"\"F1F1!\"\"F+*&*&,&*&F,F,F-F2F1*&*$F/F,F,*$)F-\" \"#F,F2!\"#F1F-F1F,F+F2" }}}{EXCHG {PARA 262 "> " 0 "" {MPLTEXT 1 0 10 "normal(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%#lnG6#* &%\"xG\"\"\",&*$)F+\"\"#F,\"\"\"F1F1!\"\"F+,$*&,&F.F1!\"\"F1F,*&F+\"\" \"F-\"\"\"F2F6" }}}{EXCHG {PARA 263 "> " 0 "" {MPLTEXT 1 0 27 "Diff(x^ (x^x),x):%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$)% \"xG)F(F(F(*&F'\"\"\",&*(F)F+,&-%#lnG6#F(F+F+F+F+F/F+F+*&F)\"\"\"F(!\" \"F+F+" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 78 "collect(%,ln(x) , simplify); #diva se na vyraz jako na polynom v promenne ln(x)" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$)%\"xG)F(F(F(,(*&)F(,&F)\" \"\"F(F.F.)-%#lnG6#F(\"\"#\"\"\"F.*&F,F4F0F.F.)F(,(F)F.F(F.!\"\"F.F." }}}{EXCHG {PARA 265 "" 0 "" {TEXT -1 22 "Derivace vyssich radu:" }} {PARA 266 "> " 0 "" {MPLTEXT 1 0 31 "Diff(exp(-x^2),x,x):%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%$expG6#,$*$)%\"xG\"\"# \"\"\"!\"\"-%\"$G6$F-F.,&F'!\"#*&F,F/F'\"\"\"\"\"%" }}}{EXCHG {PARA 267 "> " 0 "" {MPLTEXT 1 0 32 "Diff(exp(-x^2), x$5):%=value(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6$-%$expG6#,$*$)%\"xG\"\"#\" \"\"!\"\"-%\"$G6$F-\"\"&,(*&F-\"\"\"F'F7!$?\"*&)F-\"\"$F/F'F/\"$g\"*&) F-F4F/F'F/!#K" }}}{EXCHG {PARA 330 "" 0 "" {TEXT -1 31 "Derivace funkc e dane implicitne" }}}{EXCHG {PARA 413 "> " 0 "" {MPLTEXT 1 0 8 "resta rt;" }}}{EXCHG {PARA 268 "> " 0 "" {MPLTEXT 1 0 40 "alias(y=y(x)): #y \+ povazujeme za funkci x" }}}{EXCHG {PARA 269 "> " 0 "" {MPLTEXT 1 0 14 "eq:=x^2+y^2=c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,&*$)%\"xG\" \"#\"\"\"\"\"\"*$)%\"yGF*F+F,%\"cG" }}}{EXCHG {PARA 270 "> " 0 "" {MPLTEXT 1 0 11 "diff(eq,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\" xG\"\"#*&%\"yG\"\"\"-%%diffG6$F(F%F)F&\"\"!" }}}{EXCHG {PARA 271 "> " 0 "" {MPLTEXT 1 0 40 "dydx:=solve(%, diff(y,x)); # 1. derivace" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dydxG,$*&%\"xG\"\"\"%\"yG!\"\"!\"\" " }}}{EXCHG {PARA 272 "> " 0 "" {MPLTEXT 1 0 13 "diff(eq,x$2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/,(\"\"#\"\"\"*$)-%%diffG6$%\"yG%\"xGF %\"\"\"F%*&F,F&-F*6$F,-%\"$G6$F-F%F&F%\"\"!" }}}{EXCHG {PARA 273 "> " 0 "" {MPLTEXT 1 0 21 "solve(%,diff(y,x$2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&\"\"\"F&*$)-%%diffG6$%\"yG%\"xG\"\"#\"\"\"F&F/F,! \"\"!\"\"" }}}{EXCHG {PARA 274 "> " 0 "" {MPLTEXT 1 0 39 "d2ydx2:=norm al(subs(diff(y,x)=dydx,%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'d2yd x2G,$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"*$)%\"yGF+F,F-F,*$)F0\"\"$F,!\"\"!\" \"" }}}{EXCHG {PARA 275 "> " 0 "" {MPLTEXT 1 0 11 "alias(y=y):" }}} {EXCHG {PARA 332 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 333 "> " 0 "" {MPLTEXT 1 0 28 "implicitdiff(x^2+y^2,y,x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"*$)%\"yGF)F*F +F**$)F.\"\"$F*!\"\"!\"\"" }}}{EXCHG {PARA 276 "" 0 "" {TEXT -1 19 "Pa rcialni derivace:" }}{PARA 277 "> " 0 "" {MPLTEXT 1 0 36 "Diff(exp(a*x *y^2),x,y$2):%=value(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6 %-%$expG6#*(%\"aG\"\"\"%\"xGF,)%\"yG\"\"#\"\"\"F--%\"$G6$F/F0,(*&F+F1F 'F,F0**)F+F0F1F.F1F-F1F'F1\"#5**)F+\"\"$F1)F/\"\"%F1)F-F0F1F'F1F>" }}} {EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6%-%$expG6#*(%\"aG\"\"\"%\"xGF,)%\"yG\"\" #\"\"\"F--%\"$G6$F/F0,$*(F+F1F'F,,(F,F,F*\"\"&*()F+F0F1)F/\"\"%F1)F-F0 F1F0F,F0" }}}{EXCHG {PARA 279 "> " 0 "" {MPLTEXT 1 0 40 "Diff(sin(x+y) /y^4, x$5, y$2):%=value(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%%Dif fG6%*&-%$sinG6#,&%\"xG\"\"\"%\"yGF-\"\"\"*$)F.\"\"%F/!\"\"-%\"$G6$F,\" \"&-F56$F.\"\"#,(*&-%$cosGF*F/*$)F.\"\"%F/F3!\"\"*&F(F/*$)F.\"\"&F/F3 \"\")*&F=F/*$)F.\"\"'F/F3\"#?" }}}{EXCHG {PARA 280 "> " 0 "" {MPLTEXT 1 0 27 "collect(%,cos(x+y),normal);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/-%%DiffG6%*&-%$sinG6#,&%\"xG\"\"\"%\"yGF-\"\"\"*$)F.\"\"%F/!\"\"-%\" $G6$F,\"\"&-F56$F.\"\"#,&*&*&,&*$)F.F:F/F-!#?F-F--%$cosGF*F-F/*$)F.\" \"'F/F3!\"\"*&F(F/*$)F.\"\"&F/F3\"\")" }}}{EXCHG {PARA 281 "" 0 "" {TEXT -1 61 "Pokud derivujeme funkci, musime pouzit funkcniho operator u D." }}{PARA 282 "> " 0 "" {MPLTEXT 1 0 22 "g:=x->x^n*exp(sin(x));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"xG6\"6$%)operatorG%&arrow GF(*&)9$%\"nG\"\"\"-%$expG6#-%$sinG6#F.F0F(F(F(" }}}{EXCHG {PARA 283 " > " 0 "" {MPLTEXT 1 0 5 "D(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#% \"xG6\"6$%)operatorG%&arrowGF&,&*&*()9$%\"nG\"\"\"F/F0-%$expG6#-%$sinG 6#F.F0\"\"\"F.!\"\"F0*(F-F7-%$cosGF6F0F1F7F0F&F&F&" }}}{EXCHG {PARA 284 "> " 0 "" {MPLTEXT 1 0 11 "D(g)(Pi/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&*(),$%#PiG#\"\"\"\"\"'%\"nGF*F,F*-%$expG6##F*\"\"#F *\"\"\"F(!\"\"F+*(F&F2-%%sqrtG6#\"\"$F2F-F2F0" }}}{EXCHG {PARA 285 "" 0 "" {TEXT -1 102 "diff derivuje vzorec a na vystupu vraci vzorec, D d erivuje funkci a na vystupu vraci funkci.\nPriklady:" }}{PARA 286 "> \+ " 0 "" {MPLTEXT 1 0 32 "diff(cos(t),t); #derivace vzorce" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"tG!\"\"" }}}{EXCHG {PARA 287 "> " 0 "" {MPLTEXT 1 0 24 "D(cos); #derivace funkce" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%$sinG!\"\"" }}}{EXCHG {PARA 288 "> " 0 "" {MPLTEXT 1 0 80 "(D@@2)(cos); #pro druhou derivaci funkce musime pouzit operato ru skladani funkci" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%$cosG!\"\"" } }}{EXCHG {PARA 289 "> " 0 "" {MPLTEXT 1 0 41 "D(cos)(t); # derivace fu nkce v danem bode" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$sinG6#%\"tG! \"\"" }}}{EXCHG {PARA 290 "" 0 "" {TEXT -1 53 "Vsimnete si rozdilu mez i nasledujicimi dvema prikazy:" }}{PARA 291 "> " 0 "" {MPLTEXT 1 0 10 "D(cos(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"DG6#-%$cosG6#%\"tG " }}}{EXCHG {PARA 292 "" 0 "" {TEXT -1 71 "Maple povazuje cos(t) za sl ozeni funkci cos a t, spravny zapis je tedy:" }}{PARA 293 "> " 0 "" {MPLTEXT 1 0 11 "D(cos @ t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%\" @G6$,$%$sinG!\"\"%\"tG\"\"\"-%\"DG6#F*F+" }}}{EXCHG {PARA 294 "" 0 "" {TEXT -1 46 "Derivace implicitni funkce pomoci operatoru D:" }}{PARA 295 "> " 0 "" {MPLTEXT 1 0 14 "eq:=x^2+y^2=c:" }}}{EXCHG {PARA 296 "> \+ " 0 "" {MPLTEXT 1 0 6 "D(eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*& -%\"DG6#%\"xG\"\"\"F)F*\"\"#*&-F'6#%\"yGF*F/F*F+-F'6#%\"cG" }}}{EXCHG {PARA 297 "> " 0 "" {MPLTEXT 1 0 14 "solve(%,D(y));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&,&*&-%\"DG6#%\"xG\"\"\"F*F+\"\"#-F(6#%\"cG!\"\"\" \"\"%\"yG!\"\"#F0F," }}}{EXCHG {PARA 298 "> " 0 "" {MPLTEXT 1 0 30 "dy dx:=subs(D(x)=1, D(c)=0, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dyd xG,$*&%\"xG\"\"\"%\"yG!\"\"!\"\"" }}}{EXCHG {PARA 299 "> " 0 "" {MPLTEXT 1 0 11 "(D@@2)(eq);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,**&- -%#@@G6$%\"DG\"\"#6#%\"xG\"\"\"F-F.F+*$)-F*F,F+\"\"\"F+*&-F'6#%\"yGF.F 6F.F+*$)-F*F5F+F2F+-F'6#%\"cG" }}}{EXCHG {PARA 300 "> " 0 "" {MPLTEXT 1 0 19 "solve(%,(D@@2)(y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,** &--%#@@G6$%\"DG\"\"#6#%\"xG\"\"\"F.F/F,*$)-F+F-F,\"\"\"F,*$)-F+6#%\"yG F,F3F,-F(6#%\"cG!\"\"F3F8!\"\"#F " 0 "" {MPLTEXT 1 0 69 "d2ydx2:=normal(subs(D(x)=1, (D@@2)(x)=0, (D@@2)(c)=0, D(y)=dydx, %));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'d2ydx2G,$*&,&*$ )%\"xG\"\"#\"\"\"\"\"\"*$)%\"yGF+F,F-F,*$)F0\"\"$F,!\"\"!\"\"" }}} {EXCHG {PARA 302 "" 0 "" {TEXT -1 64 "Operatoru D je mozno pouzit i pr o vypocet parcialnich derivaci.\n" }}{PARA 303 "> " 0 "" {MPLTEXT 1 0 34 "h:=(x,y,z)->1/(x^2+y^2+z^2)^(1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGR6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF**&\"\"\"F/*$-% %sqrtG6#,(*$)9$\"\"#F/\"\"\"*$)9%F8F/F9*$)9&F8F/F9F/!\"\"F*F*F*" }}} {EXCHG {PARA 304 "> " 0 "" {MPLTEXT 1 0 18 "'D[1](h)'=D[1](h);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-&%\"DG6#\"\"\"6#%\"hGR6%%\"xG%\"yG% \"zG6\"6$%)operatorG%&arrowGF0,$*&9$\"\"\"*$),(*$)F6\"\"#F7F(*$)9%F=F7 F(*$)9&F=F7F(#\"\"$F=F7!\"\"!\"\"F0F0F0" }}}{EXCHG {PARA 305 "" 0 "" {TEXT -1 47 "Zde D[1](h) je parcialni derivace vzhledem k x." }}{PARA 306 "> " 0 "" {MPLTEXT 1 0 22 "'D[1,2](h)'=D[1,2](h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-&%\"DG6$\"\"\"\"\"#6#%\"hGR6%%\"xG%\"yG%\"zG6\"6 $%)operatorG%&arrowGF1,$*&*&9%F(9$F(\"\"\"*$),(*$)F9F)F:F(*$)F8F)F:F(* $)9&F)F:F(#\"\"&F)F:!\"\"\"\"$F1F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 307 "" 0 "" {TEXT -1 102 "Zde D[1,2] (h) je vlastne D[1] (D[2](h)) - smisena parcialni derivace, jednou pod le x a jednou podle y." }}{PARA 308 "> " 0 "" {MPLTEXT 1 0 22 "'D[1,1] (h)'=D[1,1](h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-&%\"DG6$\"\"\"F(6 #%\"hGR6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF0,&*&*$)9$\"\"#\"\"\" F:*$),(*$F7F:F(*$)9%F9F:F(*$)9&F9F:F(#\"\"&F9F:!\"\"\"\"$*&F:F:*$)F=# \"\"$F9F:FG!\"\"F0F0F0" }}}{EXCHG {PARA 309 "" 0 "" {TEXT -1 38 "Druha parcialni derivace vzhledem k x." }}{PARA 310 "> " 0 "" {MPLTEXT 1 0 32 "L[h]:=(D[1,1]+D[2,2]+D[3,3])(h);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>&%\"LG6#%\"hG,(R6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF.,&*&*$)9 $\"\"#\"\"\"F8*$),(*$F5F8\"\"\"*$)9%F7F8F=*$)9&F7F8F=#\"\"&F7F8!\"\"\" \"$*&F8F8*$)F;#\"\"$F7F8FF!\"\"F.F.F.F=R6%F+F,F-F.F/F.,&*&*$F?F8F8*$)F ;#\"\"&F7F8FFFGFHFMF.F.F.F=R6%F+F,F-F.F/F.,&*&*$FBF8F8*$)F;#\"\"&F7F8F FFGFHFMF.F.F.F=" }}}{EXCHG {PARA 311 "" 0 "" {TEXT -1 53 "Maple muze d erivovat i po castech definovane funkce:\n" }}}{EXCHG {PARA 334 "> " 0 "" {MPLTEXT 1 0 40 "F:=x->piecewise(x>0, sin(x), arctan(x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGR6#%\"xG6\"6$%)operatorG%&arrowG 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1 0 8 "restart;" }}}{EXCHG {PARA 317 "> " 0 "" {MPLTEXT 1 0 27 "alias(g=g(x,y(x)), y=y(x)):" }}}{EXCHG {PARA 318 "> " 0 "" {MPLTEXT 1 0 10 "diff(g,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&--&% \"DG6#\"\"\"6#%\"gG6$%\"xG%\"yGF)*&--&F'6#\"\"#F*F,F)-%%diffG6$F.F-F)F )" }}}{EXCHG {PARA 319 "> " 0 "" {MPLTEXT 1 0 25 "dydx:=solve(%,diff(y ,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dydxG,$*&--&%\"DG6#\"\"\"6 #%\"gG6$%\"xG%\"yG\"\"\"--&F*6#\"\"#F-F/!\"\"!\"\"" }}}{EXCHG {PARA 320 "> " 0 "" {MPLTEXT 1 0 21 "convert(dydx,'diff');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'&whereG6$,$*&-%%diffG6$-%\"gG6$%\"xG%#t1GF.\"\"\" -F)6$-F,6$F.%#t2GF5!\"\"!\"\"<$/F5%\"yG/F/F:" }}}{EXCHG {PARA 321 "> \+ " 0 "" {MPLTEXT 1 0 22 "subs(op(2,%),op(1,%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%%diffG6$%\"gG%\"xG\"\"\"-F&6$F(%\"yG!\"\"!\"\"" } }}{EXCHG {PARA 322 "> " 0 "" {MPLTEXT 1 0 12 "diff(g,x$2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,*--&%\"DG6$\"\"\"F)6#%\"gG6$%\"xG%\"yGF)*&- 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\"#5F.FM!\"#F)F/F.F>F)F)*$-F?6#FQF)F/#FF)FA*&*&-FH6#*&,(F(FLF6F.FMF.F)*$-F?6#,&FRF.FMFF)F)*$-F? 6#F_oF)F/#FSF-" }}}{EXCHG {PARA 343 "> " 0 "" {MPLTEXT 1 0 35 "normal( diff(rhs(%),x), 'expanded');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"x G\"\"\",&*$)F$\"\"&F%\"\"\"F*F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "infolevel[int]:=0:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Maple automaticky voli nulovou integracni konstantu:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Int(2*x*(x^2+1)^24, x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&%\"xG\"\"\"),&*$)F(\"\"# \"\"\"F)F)F)\"#CF/F.F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "% =value(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$,$*&%\"xG\"\" \"),&*$)F)\"\"#\"\"\"F*F*F*\"#CF0F/F),T*$)F)\"#IF0#\"'_Pl\"\"&*$)F)\"# YF0\"#7*$)F)\"#[F0F**$)F)\"#QF0\"%%3(*$)F)\"#SF0#\"&E1\"F8*$)F)\"#WF0 \"##**$)F)\"#UF0\"$1&*$)F)\"#;F0\"&jK%*$)F)\"#MF0FT*$)F)\"#AF0\"''Hy\" *$)F)\"#KF0\"&><)*$)F)\"#OF0\"&G#>*$)F)\"\"%F0F<*$)F)\"\"'F0FL*$)F)\" \")F0FP*$)F)F " 0 "" {MPLTEXT 1 0 20 "factor(rhs(%)+1/25);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$),&*$)%\"xG\"\"#\"\"\"\"\"\"F,F,\" #DF+#F,F-" }}}{EXCHG {PARA 344 "" 0 "" {TEXT -1 16 "Urcity integral:" }}{PARA 345 "> " 0 "" {MPLTEXT 1 0 35 "Int(x/(x^3+1), x=1..a): %=value (%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"\"\",&*$)F( \"\"$F)\"\"\"F.F.!\"\"/F(;F.%\"aG,,-%#lnG6#,&F2F.F.F.#!\"\"F--F56#,(*$ )F2\"\"#F)F.F2F9F.F.#F.\"\"'*&-%%sqrtG6#F-F)-%'arctanG6#,$*&FCF),&F2F? F9F.F.#F.F-F.FL-F56#F?FL*&FCF)%#PiGF.#F9\"#=" }}}{EXCHG {PARA 346 "> \+ " 0 "" {MPLTEXT 1 0 36 "Int(1/((1+x^2)*(1+2*x^2)), x=0..1): " }}} {EXCHG {PARA 347 "> " 0 "" {MPLTEXT 1 0 11 "%=value(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(*&,&\"\"\"F+*$)%\"xG\"\"#F(F +\"\"\",&F+F+F,F/\"\"\"!\"\"/F.;\"\"!F+,&%#PiG#!\"\"\"\"%*&-%%sqrtG6#F /F(-%'arctanG6#*$F=F(F+F+" }}}{EXCHG {PARA 348 "" 0 "" {TEXT -1 60 "Ma ple kontroluje nespojitosti integrandu na danem intervalu." }}{PARA 349 "> " 0 "" {MPLTEXT 1 0 30 "Int(1/x, x=-1..1): %=value(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(%\"xG!\"\"/F);!\" \"\"\"\"-%$intGF&" }}}{EXCHG {PARA 350 "" 0 "" {TEXT -1 97 "Nejsou spl neny podminky fund. theoremu -- v bode 0 ma zadana funkce neodstranite lnou nespojitost." }}{PARA 351 "" 0 "" {TEXT -1 20 "Nevlastni integral y:" }}{PARA 352 "> " 0 "" {MPLTEXT 1 0 56 "Int(t^4*ln(t)^2/(1+3*t^2)^3 , t=0..infinity): %=value(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%$I ntG6$*&*&)%\"tG\"\"%\"\"\")-%#lnG6#F*\"\"#F,F,*$),&\"\"\"F5*$)F*F1F,\" \"$\"\"$F,!\"\"/F*;\"\"!%)infinityG,**&-%%sqrtG6#F8F,%#PiGF5#F5\"$;#*& FAF,)FDF8F,#F5\"$w&*(FDF,FAF,-F/6#F8F5#!\"\"\"$3\"*(FDF,FAF,)FLF1F,FI " }}}{EXCHG {PARA 353 "" 0 "" {TEXT -1 97 "V pripade, ze Maple neni sc hopen nalezt symbolicke reseni, muzeme pouzit numerickeho integrovani: " }}{PARA 354 "> " 0 "" {MPLTEXT 1 0 28 "int(exp(arcsin(x)), x=0..1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$-%$expG6#-%'arcsinG6#%\"x G/F,;\"\"!\"\"\"" }}}{EXCHG {PARA 355 "> " 0 "" {MPLTEXT 1 0 9 "evalf( %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!pQ_!>!\"*" }}}{EXCHG {PARA 356 "" 0 "" {TEXT -1 44 "Nekdy je vyhodne pri reseni Maplu asist ovat:" }}{PARA 357 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}{PARA 7 "" 1 "" {TEXT -1 29 "Warning, new definition for D" }}}{EXCHG {PARA 358 "> " 0 "" {MPLTEXT 1 0 20 "Int(sqrt(9-x^2), x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%$IntG6$*$-%%sqrtG6#,&\"\"*\"\"\"*$)%\"xG\"\"#\"\"\" !\"\"F1F/" }}}{EXCHG {PARA 359 "> " 0 "" {MPLTEXT 1 0 45 "changevar(x= 3*sin(t), Int(sqrt(9-x^2), x),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %$IntG6$,$*&-%%sqrtG6#,&\"\"*\"\"\"*$)-%$sinG6#%\"tG\"\"#\"\"\"!\"*F5- %$cosGF2F-\"\"$F3" }}}{EXCHG {PARA 360 "> " 0 "" {MPLTEXT 1 0 9 "value (%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$sinG6#%\"tG\"\"\"-%%sqr tG6#,&F)F)*$)F%\"\"#\"\"\"!\"\"F1#\"\"*F0-%'arcsinG6#F%F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "subs(t=arcsin(x/3), %);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,&*&-%$sinG6#-%'arcsinG6#,$%\"xG#\"\"\"\"\"$ F.-%%sqrtG6#,&F.F.*$)F%\"\"#\"\"\"!\"\"F7#\"\"*F6-F)6#F%F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"-%%sqrtG6#,&\"\"*F&*$)F%\"\"#\"\"\"!\"\" F/#F&F.-%'arcsinG6#,$F%#F&\"\"$#F+F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Pro metodu per - partes:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "i:=Int((x^2+1)*ln(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"iG-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"F/F/F/-%#lnG6#F,F/F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "i=intparts(i, ln(x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"\"\" \"F.F.F.-%#lnG6#F+F.F+,&*&F/F-,&*$)F+\"\"$F-#F.F7F+F.F.F.-F%6$*&F4F-F+ !\"\"F+!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Druhym argumentem prikazu intparts je ta cast integrandu, kterou budeme derivovat." }}} {EXCHG {PARA 0 "" 0 "" {URLLINK 17 "Postup vypoctu (od Maple 8)" 4 "ht tp://cgi.math.muni.cz/~xsrot/int/uvod.cgi?cnt=yes" "" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 361 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 362 "" 0 "" {TEXT -1 27 "Konecne a nekonecne soucty:" }}{PARA 363 "> " 0 "" {MPLTEXT 1 0 30 "Sum(k^7, k=1..20): %=value(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*$)%\"kG\"\"(\"\"\"/F);\"\" \"\"#?\"++nGxQ" }}}{EXCHG {PARA 364 "> " 0 "" {MPLTEXT 1 0 29 "Sum(k^7 , k=1..n): %=value(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*$ )%\"kG\"\"(\"\"\"/F);\"\"\"%\"nG,,*$),&F/F.F.F.\"\")F+#F.F4*$)F3F*F+#! \"\"\"\"#*$)F3\"\"'F+#F*\"#7*$)F3\"\"%F+#!\"(\"#C*$)F3F:F+#F.F?" }}} {EXCHG {PARA 365 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*$)%\"kG\"\"(\"\"\"/F);\"\"\"%\"nG,$*()F /\"\"#F+,,*$)F/\"\"%F+\"\"$*$)F/F8F+\"\"'*$F2F+!\"\"F/!\"%F3F.F.),&F/F .F.F.F3F+#F.\"#C" }}}{EXCHG {PARA 366 "> " 0 "" {MPLTEXT 1 0 42 "Sum(1 /(k^2-4), k=3..infinity): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*&\"\"\"F(,&*$)%\"kG\"\"#F(\"\"\"!\"%F.!\"\"/F,;\"\"$%)in finityG#\"#D\"#[" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Tayloruv ro zvoj" }}{EXCHG {PARA 367 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 41 "taylo r(sin(tan(x))-tan(sin(x)), x=0, 25);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#+7%\"xG#!\"\"\"#I\"\"(#!#H\"$c(\"\"*#!%8>\"&+c(\"#6#!#&*\"%#R(\"#8#! *p)[6J\",+?V'[a\"#:#!)2K>5\"+gX\"*eV\"#<#!+j$3Tm\"\".+[Ooa!>\"#>#!.,+Y bv4#\"1+?bv(=Gg(\"#@#!0$)[2DYpu$\"4++w&[A0[!p'\"#B-%\"OG6#\"\"\"\"#D" }}}{EXCHG {PARA 368 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'seriesG" }}}{EXCHG {PARA 369 "> " 0 "" {MPLTEXT 1 0 10 "order(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" } }}{EXCHG {PARA 370 "> " 0 "" {MPLTEXT 1 0 6 "Order;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 371 "> " 0 "" {MPLTEXT 1 0 28 "Order:=3: taylor(f(x), x=a);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#++,&% \"xG\"\"\"%\"aG!\"\"-%\"fG6#F'\"\"!--%\"DG6#F*F+\"\"\",$---%#@@G6$F/\" \"#F0F+#F&F8\"\"#-%\"OG6#F&\"\"$" }}}{EXCHG {PARA 372 "> " 0 "" {MPLTEXT 1 0 35 "sin_series:=taylor(sin(x), x=0, 6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+sin_seriesG++%\"xG\"\"\"\"\"\"#!\"\"\"\"'\"\"$#F' \"$?\"\"\"&-%\"OG6#F'\"\"'" }}}{EXCHG {PARA 373 "" 0 "" {TEXT -1 84 "I kdyz struktura rozvoje nam pripomina polynom, interni datova reprezen tace je jina:" }}{PARA 374 "> " 0 "" {MPLTEXT 1 0 22 "subs(x=2, sin_se ries);" }}{PARA 8 "" 1 "" {TEXT -1 37 "Error, invalid substitution in \+ series" }}}{EXCHG {PARA 375 "> " 0 "" {MPLTEXT 1 0 15 "op(sin_series); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6*\"\"\"F##!\"\"\"\"'\"\"$#F#\"$?\" \"\"&-%\"OG6#F#F&" }}}{EXCHG {PARA 376 "> " 0 "" {MPLTEXT 1 0 22 "sin_ series*sin_series;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)++%\"xG\"\"\" \"\"\"#!\"\"\"\"'\"\"$#F'\"$?\"\"\"&-%\"OG6#F'\"\"'\"\"#\"\"\"" }}} {EXCHG {PARA 377 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)++%\"xG\"\"\"\"\"\"#!\"\"\"\"'\"\"$#F'\"$?\"\" \"&-%\"OG6#F'\"\"'\"\"#\"\"\"" }}}{EXCHG {PARA 378 "> " 0 "" {MPLTEXT 1 0 12 "taylor(%,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+)%\"xG\"\"\" \"\"##!\"\"\"\"$\"\"%-%\"OG6#F%\"\"'" }}}{EXCHG {PARA 379 "> " 0 "" {MPLTEXT 1 0 17 "readlib(mtaylor);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# R6\"6*%\"fG%\"kG%\"vG%\"mG%\"nG%\"sG%\"tG%\"wG6#%aoCopyright~(c)~1991~ by~the~University~of~Waterloo.~All~rights~reserved.GF$C2>8$&9\"6#\"\" \">8&&F46#\"\"#@&-%%typeG6$F8%$setG>F87#-%#opG6#F84-F>6$F8%%listG>F87# F8@$4-F>6$F8-FI6#<$/%%nameG%*algebraicGFT-%&ERRORG6#%Ginvalid~2nd~argu ment~(expansion~point)G>8)-%$mapG6$R6#%\"xGF$F$F$@%-F>6$9$%\"=G-%$rhsG 6#F_o\"\"!F$F$F$F8>F8-Fgn6$RFjnF$F$F$@%F]o-%$lhsGFcoF_oF$F$F$F8>8'-%%n opsGFE@$0F]p-F_p6#<#FC-FW6#%Hvariables~(2nd~argument)~must~be~uniqueG@ %/9#F;>8(\"\"'>F\\q&F46#\"\"$@%/Fjp\"\"%>8+&F46#Fdq>Ffq7#-%\"$G6$F6F]p @$4-F>6$F8<$-F@6#FT-FIFdr-FW6#%O2nd~argument~(the~variable(s))~must~be ~a~namesG@$34-F>6$F\\q%*nonnegintG0F\\q%)infinityG-FW6#%X3rd~argument~ (the~order)~must~be~a~non-negative~integerG@$54-F>6$Ffq-FI6#%'posintG0 -F_p6#FfqF]p-FW6#%en4th~argument~(weights)~must~be~a~list~of~positive~ integersG>F2-%%subsG6$7#-%$seqG6$/&F86#8%,&*&F[uF6)8*&FfqF\\uF6F6&FenF \\uF6/F]u;F6F]pF2>F2-Fgn6&%(collectG-Fdt6$/-%\"OGF5Fdo-%'taylorG6%F2Fa uF\\qF8.%,distributedG>F2-Fdt6$7#-Fht6$/F[u,&F[uF6Fcu!\"\"Fdu-Fdt6$/Fa uF6F2F$F$F$" }}}{EXCHG {PARA 380 "" 0 "" {TEXT -1 85 "mtaylor pocita T aylorovy rozvoje i pro funkce vice promennych a vysledkem je polynom. " }}{PARA 381 "> " 0 "" {MPLTEXT 1 0 23 "mtaylor(sin(x), x=0,6);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"xG\"\"\"*$)F$\"\"$\"\"\"#!\"\"\" \"'*$)F$\"\"&F)#F%\"$?\"" }}}{EXCHG {PARA 382 "> " 0 "" {MPLTEXT 1 0 13 "subs(x=2, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#9\"#:" }}} {EXCHG {PARA 383 "> " 0 "" {MPLTEXT 1 0 13 "whattype(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"+G" }}}{EXCHG {PARA 384 "" 0 "" {TEXT -1 76 "Muzeme urcit koeficienty u danych mocnin x bez nutnosti pocitat cely \+ rozvoj:" }}{PARA 385 "> " 0 "" {MPLTEXT 1 0 18 "readlib(coeftayl);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#R6%%\"eG%$eqnG%\"kG6(%\"iG%\"xG%&alpha G%\"cG%\"rG%#mtG6#%aoCopyright~(c)~1990~by~the~University~of~Waterloo. ~All~rights~reserved.G6\"@)509#\"\"$4-%%typeG6$9%%\"=G-%&ERRORG6#%Ewro ng~number~(or~type)~of~parametersG33-F96$-%#opG6$\"\"\"F;%%nameG-F96$9 &%(integerG1\"\"!FLC%@%/FLFO>8'9$>FT-%%diffG6$FU-%\"$G6$FEFL>8(-%*trap errorG6#*&-%%subsG6$F;FT\"\"\"-%*factorialG6#FL!\"\"@%0Fhn%*lasterrorG 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{PARA 388 "> " 0 "" {MPLTEXT 1 0 20 "diff(sin_ser ies, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\"\"\"\"\"!#!\"\"\" \"#\"\"##F%\"#C\"\"%-%\"OG6#F%\"\"&" }}}{EXCHG {PARA 389 "> " 0 "" {MPLTEXT 1 0 25 "integrate(sin_series, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG#\"\"\"\"\"#\"\"##!\"\"\"#C\"\"%#F&\"$?(\"\"'-% \"OG6#F&\"\"(" }}}{EXCHG {PARA 390 "> " 0 "" {MPLTEXT 1 0 31 "convert( sin_series, 'polynom');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"xG\"\" \"*$)F$\"\"$\"\"\"#!\"\"\"\"'*$)F$\"\"&F)#F%\"$?\"" }}}{EXCHG {PARA 391 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 392 "> " 0 "" {MPLTEXT 1 0 65 "with(powseries); #procedury, slouzici k praci s mocni nnymi radami" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#77%(composeG%(evalpowG %(inverseG%*multconstG%)multiplyG%)negativeG%'powaddG%'powcosG%*powcre ateG%(powdiffG%'powexpG%'powintG%'powlogG%(powpolyG%'powsinG%)powsolve G%(powsqrtG%)quotientG%*reversionG%)subtractG%(tpsformG" }}}{EXCHG {PARA 393 "> " 0 "" {MPLTEXT 1 0 23 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