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}0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 390 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 "" 0 391 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 "" 0 392 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 "" 0 393 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 "" 0 394 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 "" 0 395 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 "" 0 396 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 "" 0 397 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 "" 0 398 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 "" 0 399 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 "" 0 400 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 "" 0 401 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 "" 0 402 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 "" 0 403 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 "" 0 404 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 "" 0 405 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 "" 0 406 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 1 {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$2):%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%DiffG6
%-%$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$2):%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%%Dif
fG6%*&-%$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,$*&%\"xG\"\"\"%\"yG!\"\"!\"\"" }}}{EXCHG {PARA 299 "> " 0 "" 
{MPLTEXT 1 0 11 "(D@@2)(eq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,**&-
-%#@@G6$%\"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<F," }}}{EXCHG {PARA 301 "> " 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 84 "D[1,2](h) = proc (x, y, z) options operator, arrow; 3
*y*x/((x^2+y^2+z^2)^(5/2)) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/R6
%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF),$*&*&9%\"\"\"9$F1\"\"\"*$),
(*$)F2\"\"#F3F1*$)F0F9F3F1*$)9&F9F3F1#\"\"&F9F3!\"\"\"\"$F)F)F)R6%F&F'
F(F)F*F)F-F)F)F)" }}}{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 11 "" 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=#
\"\"$F9F:FG!\"\"F0F0F0" }}}{EXCHG {PARA 309 "" 0 "" {TEXT -1 38 "Druha
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1#=`M#>#G*)*F`r7$Fat$\"1hJc'4eO!)*F`r7$$\"1q!*RYC%Q-$F`r$\"123i>=HY&*F
`r7$Fft$\"1U/u(yrf=*F`r7$F[u$\"1QGy]>:D$)F`r7$F`u$\"1hAY/Uo#>(F`r7$Feu
$\"1KSx%Qdsq&F`r7$Fju$\"1d!)>%\\.Z+%F`r7$F_v$\"1,*\\hQE71$F`r7$Fdv$\"1
\\F2^@g'3#F`r7$F^w$\"1WjZ>tu!4\"F`r7$Fhw$\"1>K\\GPWz$)F]t7$F\\y$!14n&H
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$F_[l$!16jCb:(\\#)*F`r7$$\"12WTr(p=+$F*$!1f/v!GYD!**F`r7$$\"1J*f$Q*=&
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*****F`r7$$\"1mjZGHp&>$F*$!15tEq$p`)**F`r7$$\"1a<q%eolC$F*$!1!\\C0&3&
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7$F\\^l$!1F#\\5ucb(>F`r7$F`_l$!1R'4q@Z?<*F]t7$Fd`l$\"1c_%3&3&)z=F`r7$F
^al$\"154/NfvxPF`r7$Fcal$\"1k0-e3p!\\&F`r7$Fhal$\"11mi+u#z*pF`r7$F]bl$
\"1>heb/9%H)F`r7$Fbbl$\"1&QB;X(*)\\#*F`r7$$\"1ufw#QI6*fF*$\"1fQBDCaw&*
F`r7$Fgbl$\"1GU:Izy6)*F`r7$$\"1r)QrdHx8'F*$\"1XiyN&*R%*)*F`r7$$\"1qJEv
ff'='F*$\"1_M+g()Q`**F`r7$$\"1puQtBYNiF*$\"1I*)**oZh))**F`r7$F\\cl$\"0
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$$\"1Xferk;%e'F*$\"1yk?a2Y]&*F`r7$Ffcl$\"1RVeBe*p?*F`r7$F[dl$\"1<%Ggfv
!e#)F`r7$F`dl$\"1UIFhHp&)pF`r7$Fedl$\"1g'H>h')Qd&F`r7$Fjdl$\"1fA[\"GRw
(RF`r7$F_el$\"1HV?&4&)***HF`r7$Fdel$\"1XRwA1n*)>F`r7$F^fl$\"1i\"*o?(\\
pd*Fg[m7$Fhfl$!1BayqFpq%)F]t7$F\\hl$!1#=y%H*R'R>F`r7$Ffhl$!1j$*\\Dt8FP
F`r7$F[il$!1(GE]d8))[&F`r7$F`il$!1m(>JUSO.(F`r7$Feil$!1<$fvl#o_#)F`r7$
Fjil$!19sj[i&H<*F`r7$$\"1)\\q%>qg<\"*F*$!128\"\\'y#>`*F`r7$F_jl$!1h)Rr
;c5z*F`r7$$\"1Z-q![#>r#*F*$!1^I*)f\"*G#))*F`r7$$\"1)\\VWj(QA$*F*$!1)*)
[])oiZ**F`r7$$\"1\\n=)y#et$*F*$!1NH]L\")*o)**F`r7$Fdjl$F_[mF`[m-Fjjl6&
F\\[mF`[mF][mF`[m-%+AXESLABELSG6$%!GFfbn-%%VIEWG6$;$!+izxC%*!\"*$\"+iz
xC%*F]cn%(DEFAULTG" 2 264 264 264 2 0 1 0 2 9 0 4 2 1.000000 
45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 16329 
-7415 0 0 0 0 0 0 }}}{EXCHG {PARA 315 "" 0 "" {TEXT -1 72 "Nasledujici
 priklad ilustruje moznosti Maplu pri symbolickem derivovani:" }}
{PARA 316 "> " 0 "" {MPLTEXT 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$-%\"gG
6$%\"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$2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*--&%\"DG6$\"\"\"F)6#%\"gG6$
%\"xG%\"yGF)*&--&F'6$F)\"\"#F*F,F)-%%diffG6$F.F-F)F)*&,&F0F)*&--&F'6$F
4F4F*F,F)F5\"\"\"F)F)F5F?F)*&--&F'6#F4F*F,F)-F66$F.-%\"$G6$F-F4F)F)" }
}}{EXCHG {PARA 323 "> " 0 "" {MPLTEXT 1 0 21 "solve(%,diff(y,x$2));" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,(--&%\"DG6$\"\"\"F+6#%\"gG6$%\"x
G%\"yGF+*&--&F)6$F+\"\"#F,F.F+-%%diffG6$F0F/F+F6*&--&F)6$F6F6F,F.F+)F7
F6\"\"\"F+F@--&F)6#F6F,F.!\"\"!\"\"" }}}{EXCHG {PARA 324 "> " 0 "" 
{MPLTEXT 1 0 39 "d2ydx2:=normal(subs(diff(y,x)=dydx,%));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%'d2ydx2G,$*&,(*&--&%\"DG6$\"\"\"F.6#%\"gG6$%\"
xG%\"yGF.)--&F,6#\"\"#F/F1F9\"\"\"F.*(--&F,6$F.F9F/F1F.--&F,6#F.F/F1F.
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{EXCHG {PARA 325 "> " 0 "" {MPLTEXT 1 0 42 "convert(%,'diff'): subs(op
(2,%), op(1,%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,(*&-%%diffG6$
%\"gG-%\"$G6$%\"xG\"\"#\"\"\")-F(6$F*%\"yGF/\"\"\"F0*(-F(6$F2F.F0-F(6$
F*F.F0F2F0!\"#*&-F(6$F2F4F0)F9F/F5F0F5*$)F2\"\"$F5!\"\"!\"\"" }}}
{EXCHG {PARA 326 "> " 0 "" {MPLTEXT 1 0 11 "alias(g=g):" }}}{EXCHG 
{PARA 327 "> " 0 "" {MPLTEXT 1 0 23 "g:=(x,y)->exp(x^2+y^2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF
)-%$expG6#,&*$)9$\"\"#\"\"\"\"\"\"*$)9%F4F5F6F)F)F)" }}}{EXCHG {PARA 
328 "> " 0 "" {MPLTEXT 1 0 5 "dydx;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,$*&%\"xG\"\"\"%\"yG!\"\"!\"\"" }}}{EXCHG {PARA 329 "> " 0 "" 
{MPLTEXT 1 0 15 "normal(d2ydx2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$
*&,&*$)%\"xG\"\"#\"\"\"\"\"\"*$)%\"yGF)F*F+F**$)F.\"\"$F*!\"\"!\"\"" }
}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "Integrace a sumace" }}{EXCHG 
{PARA 337 "" 0 "" {TEXT -1 190 "Maple pouziva k integraci specialni al
goritmy (a to tehdy, pokud zakladni metody(per partes, rozklad na parc
. zlomky, ...)) selhavaji.\nProcedura Int integral nevyhodnocuje, pouz
e prepisuje.\n" }}{PARA 338 "> " 0 "" {MPLTEXT 1 0 29 "Int(x/(x^3+1), \+
x):%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"
\"\",&*$)F(\"\"$F)\"\"\"F.F.!\"\"F(,(-%#lnG6#,&F(F.F.F.#!\"\"F--F26#,(
*$)F(\"\"#F)F.F(F6F.F.#F.\"\"'*&-%%sqrtG6#F-F)-%'arctanG6#,$*&,&F(F<F6
F.F.F@F)#F.F-F.FI" }}}{EXCHG {PARA 339 "> " 0 "" {MPLTEXT 1 0 16 "diff
(rhs(%), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"\"F%,&%\"xG\"
\"\"F(F(!\"\"#!\"\"\"\"$*&,&F'\"\"#F+F(F%,(*$)F'F/F%F(F'F+F(F(F)#F(\"
\"'*&F%F%,&F(F(*$)F.F/F%#F(F,F)#F/F," }}}{EXCHG {PARA 340 "" 0 "" 
{TEXT -1 62 "rhs() odkazuje na pravou stranu rovnice, lhs() na levou s
tranu" }}{PARA 341 "> " 0 "" {MPLTEXT 1 0 21 "normal(%,'expanded');" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",&*$)F$\"\"$F%\"\"\"F*F*
!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "infolevel[int]:=2:
" }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 342 "> " 0 
"" {MPLTEXT 1 0 29 "Int(x/(x^5+1),x): %=value(%);" }}{PARA 6 "" 1 "" 
{TEXT -1 48 "int/indef1:   first-stage indefinite integration" }}
{PARA 6 "" 1 "" {TEXT -1 44 "int/ratpoly:   rational function integrat
ion" }}{PARA 6 "" 1 "" {TEXT -1 44 "int/ratpoly:   rational function i
ntegration" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"\"\",
&*$)F(\"\"&F)\"\"\"F.F.!\"\"F(,0-%#lnG6#,&F(F.F.F.#!\"\"F--F26#,**$)F(
\"\"#F)!\"#F(F.*&-%%sqrtG6#F-F)F(F.F.F=F.#F.\"#?*&F7F.F?F)#F6FC*&*&-%'
arctanG6#*&,(F(!\"%F.F.*$F?F)F.F)*$-F@6#,&\"#5F.FNF=F)F/F.F?F)F)*$-F@6
#FRF)F/#F=F--F26#,*F:F<F(F6F>F.F<F.FB*&FXF.F?F)FB*&*&-FI6#*&,(F(\"\"%F
6F.FNF.F)*$-F@6#,&FSF.FNF<F)F/F.F?F)F)*$-F@6#F`oF)F/FW" }}}{EXCHG 
{PARA 343 "> " 0 "" {MPLTEXT 1 0 35 "normal(diff(rhs(%),x), 'expanded'
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\",&*$)F$\"\"&F%\"\"
\"F*F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "infolevel[in
t]:=0:" }}}{EXCHG {PARA 344 "" 0 "" {TEXT -1 16 "Urcity integral:" }}
{PARA 345 "> " 0 "" {MPLTEXT 1 0 35 "Int(x/(x^3+1), x=1..a): %=value(%
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"\"\",&*$)F(\"
\"$F)\"\"\"F.F.!\"\"/F(;F.%\"aG,,-%#lnG6#,&F2F.F.F.#!\"\"F--F56#,(*$)F
2\"\"#F)F.F2F9F.F.#F.\"\"'*&-%%sqrtG6#F-F)-%'arctanG6#,$*&FCF),&F2F?F9
F.F.#F.F-F.FL-F56#F?FL*&FCF)%#PiGF.#F9\"#=" }}}{EXCHG {PARA 346 "> " 
0 "" {MPLTEXT 1 0 36 "Int(1/((1+x^2)*(1+2*x^2)), x=0..1): " }}}{EXCHG 
{PARA 347 "> " 0 "" {MPLTEXT 1 0 11 "%=value(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(*&,&\"\"\"F+*$)%\"xG\"\"#F(F+\"\"\"
,&F+F+F,F/\"\"\"!\"\"/F.;\"\"!F+,&%#PiG#!\"\"\"\"%*&-%%sqrtG6#F/F(-%'a
rctanG6#*$F=F(F+F+" }}}{EXCHG {PARA 348 "" 0 "" {TEXT -1 60 "Maple kon
troluje nespojitosti integrandu na danem intervalu." }}{PARA 349 "> " 
0 "" {MPLTEXT 1 0 30 "Int(1/x, x=-1..1): %=value(%);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(%\"xG!\"\"/F);!\"\"\"\"\"-%$intG
F&" }}}{EXCHG {PARA 350 "" 0 "" {TEXT -1 97 "Nejsou splneny podminky f
und. theoremu -- v bode 0 ma zadana funkce neodstranitelnou nespojitos
t." }}{PARA 351 "" 0 "" {TEXT -1 20 "Nevlastni integraly:" }}{PARA 
352 "> " 0 "" {MPLTEXT 1 0 56 "Int(t^4*ln(t)^2/(1+3*t^2)^3, t=0..infin
ity): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&*&)%
\"tG\"\"%\"\"\")-%#lnG6#F*\"\"#F,F,*$),&\"\"\"F5*$)F*F1F,\"\"$\"\"$F,!
\"\"/F*;\"\"!%)infinityG,**&-%%sqrtG6#F8F,%#PiGF5#F5\"$;#*&FAF,)FDF8F,
#F5\"$w&*(FDF,FAF,-F/6#F8F5#!\"\"\"$3\"*(FDF,FAF,)FLF1F,FI" }}}{EXCHG 
{PARA 353 "" 0 "" {TEXT -1 97 "V pripade, ze Maple neni schopen nalezt
 symbolicke reseni, muzeme pouzit numerickeho integrovani:" }}{PARA 
354 "> " 0 "" {MPLTEXT 1 0 28 "int(exp(arcsin(x)), x=0..1);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%$intG6$-%$expG6#-%'arcsinG6#%\"xG/F,;\"\"!
\"\"\"" }}}{EXCHG {PARA 355 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!pQ_!>!\"*" }}}{EXCHG {PARA 356 "
" 0 "" {TEXT -1 44 "Nekdy je vyhodne pri reseni Maplu asistovat:" }}
{PARA 357 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 
358 "> " 0 "" {MPLTEXT 1 0 20 "Int(sqrt(9-x^2), x);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%$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 "" {TEXT -1 24 "Pro metodu per - partes:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "i:=Int((x^2+1)*ln(x), x=1..2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"
\"\"\"F/F/F/-%#lnG6#F,F//F,;F/F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "i=intparts(i, ln(x));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"F.F.F.-%#lnG6#F+F./F+;F.F
,,&-F06#F,#\"#9\"\"$-F%6$*&,&*$)F+F9F-#F.F9F+F.F-F+!\"\"F2!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "i=value(lhs(%));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"F.F.F
.-%#lnG6#F+F./F+;F.F,,&-F06#F,#\"#9\"\"$#!#;\"\"*F." }}}{EXCHG {PARA 
0 "" 0 "" {URLLINK 17 "Postup vypoctu (od Maple 8)" 4 "http://cgi.math
.muni.cz/~xsrot/int/uvod.cgi?cnt=yes" "" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 361 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 362 "" 
0 "" {TEXT -1 27 "Konecne a nekonecne soucty:" }}{PARA 363 "> " 0 "" 
{MPLTEXT 1 0 30 "Sum(k^7, k=1..20): %=value(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$SumG6$*$)%\"kG\"\"(\"\"\"/F);\"\"\"\"#?\"++nGxQ" }}
}{EXCHG {PARA 364 "> " 0 "" {MPLTEXT 1 0 29 "Sum(k^7, k=1..n): %=value
(%);" }}{PARA 11 "" 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..infin
ity): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$SumG6$*&\"\"
\"F(,&*$)%\"kG\"\"#F(\"\"\"!\"%F.!\"\"/F,;\"\"$%)infinityG#\"#D\"#[" }
}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Tayloruv rozvoj" }}{EXCHG 
{PARA 367 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 41 "taylor(sin(tan(x))-t
an(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$3Tm\"\".+[Ooa!>\"#>#!.,+Ybv4#\"1+?bv(=Gg
(\"#@#!0$)[2DYpu$\"4++w&[A0[!p'\"#B-%\"OG6#\"\"\"\"#D" }}}{EXCHG 
{PARA 368 "> " 0 "" {MPLTEXT 1 0 12 "whattype(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%'seriesG" }}}{EXCHG {PARA 369 "> " 0 "" {MPLTEXT 1 0 
10 "order(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}{EXCHG 
{PARA 370 "> " 0 "" {MPLTEXT 1 0 6 "Order;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 371 "> " 0 "" {MPLTEXT 1 0 28 "O
rder:=3: taylor(f(x), x=a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++,&%\"
xG\"\"\"%\"aG!\"\"-%\"fG6#F'\"\"!--%\"DG6#F*F+\"\"\",$---%#@@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#\"\"(" }}}{EXCHG {PARA 376 "> " 0 "" {MPLTEXT 1 0 22 "s
in_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~Un
iversity~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#<$%%nameG/FS%*algebraicG-%&ERRORG6#%Ginvalid~2nd~argument~(expa
nsion~point)G>8)-%$mapG6$R6#%\"xGF$F$F$@%-F>6$9$%\"=G-%$rhsG6#F_o\"\"!
F$F$F$F8>F8-Fgn6$RFjnF$F$F$@%F]o-%$lhsGFcoF_oF$F$F$F8>8'-%%nopsGFE@$0F
]p-F_p6#<#FC-FW6#%Hvariables~(2nd~argument)~must~be~uniqueG@%/9#F;>8(
\"\"'>F\\q&F46#\"\"$@%/Fjp\"\"%>8+&F46#Fdq>Ffq7#-%\"$G6$F6F]p@$4-F>6$F
8<$-FI6#FS-F@Fdr-FW6#%O2nd~argument~(the~variable(s))~must~be~a~namesG
@$34-F>6$F\\q%*nonnegintG0F\\q%)infinityG-FW6#%X3rd~argument~(the~orde
r)~must~be~a~non-negative~integerG@$54-F>6$Ffq-FI6#%'posintG0-F_p6#Ffq
F]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%F2FauF\\qF8.%
,distributedG>F2-Fdt6$7#-Fht6$/F[u,&F[uF6Fcu!\"\"Fdu-Fdt6$/FauF6F2F$F$
F$" }}}{EXCHG {PARA 380 "" 0 "" {TEXT -1 85 "mtaylor pocita Taylorovy \+
rozvoje i pro funkce vice promennych a vysledkem je polynom." }}{PARA 
381 "> " 0 "" {MPLTEXT 1 0 23 "mtaylor(sin(x), x=0,6);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(%\"xG\"\"\"*$)F$\"\"$\"\"\"#!\"\"\"\"'*$)F$\"\"&
F)#F%\"$?\"" }}}{EXCHG {PARA 382 "> " 0 "" {MPLTEXT 1 0 13 "subs(x=2, \+
%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#9\"#:" }}}{EXCHG {PARA 383 
"> " 0 "" {MPLTEXT 1 0 13 "whattype(%%);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%\"+G" }}}{EXCHG {PARA 384 "" 0 "" {TEXT -1 76 "Muzeme urcit koe
ficienty u danych mocnin x bez nutnosti pocitat cely rozvoj:" }}{PARA 
385 "> " 0 "" {MPLTEXT 1 0 18 "readlib(coeftayl);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#R6%%\"eG%$eqnG%\"kG6(%\"iG%\"xG%&alphaG%\"cG%\"rG%#mtG6
#%aoCopyright~(c)~1990~by~the~University~of~Waterloo.~All~rights~reser
ved.G6\"@)509#\"\"$4-%%typeG6$9%%\"=G-%&ERRORG6#%Ewrong~number~(or~typ
e)~of~parametersG33-F96$-%#opG6$\"\"\"F;%%nameG-F96$9&%(integerG1\"\"!
FLC%@%/FLFO>8'9$>FT-%%diffG6$FU-%\"$G6$FEFL>8(-%*traperrorG6#*&-%%subs
G6$F;FT\"\"\"-%*factorialG6#FL!\"\"@%0Fhn%*lasterrorG-%%evalG6#Fhn*&-%
&limitG6$FTF;F`oFaoFdo333333-F96$FE%%listG-F96$-FF6$\"\"#F;Fgp-F96$FLF
gp/-%%nopsG6#FE-FaqFco/-Faq6#FjpFcq2FOFcq4-%$hasG6$-%$mapG6$R6#%\"nGF1
F1F13-F96$FUFM1FOFUF1F1F1FL%&falseGC)>FTFU>8%FE>8&Fjp@$0-%(convertG6$F
L%\"+GFO?(8$FHFHFcq%%trueG?(F1FHFH&FL6#FdsFes>FT-FX6$FT&FjrFhs>Fhn-Fjn
6#-F^o6$<#-Fen6$./F\\t&F\\sFhs/.Fds;FHFcqFT@%/FhnFgoC$>Fhn-F]p6$FTFbt@
$5/Fhn.%*undefinedG-Fjq6$Fhn.F]pC'-%(readlibG6#.%(mtaylorG>8)-Fjn6#-F^
v6$FU7#-%$seqG6$/-FF6$Fds-%$lhsG6#F;-FF6$Fds-%$rhsGF^w/Fds;FH-Faq6#F\\
w@$/F`vFgo-F>6#%0unable~to~do~itG?(FdsFHFHFcqFes>F`v-%&coeffG6%F`vF\\w
-FF6$FdsFL>FhnF`v>FhnFho@%/FhnFOFhn*&FhnF`o-%(productG6$.-Fbo6#FgsFhtF
do-F>6#%9wrong~type~of~parametersGF1F1F1" }}}{EXCHG {PARA 386 "> " 0 "
" {MPLTEXT 1 0 26 "coeftayl(sin(x), x=0, 19);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6##!\"\"\"3+?$)3/5X;7" }}}{EXCHG {PARA 387 "> " 0 "" 
{MPLTEXT 1 0 11 "sin_series;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"x
G\"\"\"\"\"\"#!\"\"\"\"'\"\"$#F%\"$?\"\"\"&-%\"OG6#F%\"\"(" }}}{EXCHG 
{PARA 388 "> " 0 "" {MPLTEXT 1 0 20 "diff(sin_series, x);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#++%\"xG\"\"\"\"\"!#!\"\"\"\"#\"\"##F%\"#C\"\"%-
%\"OG6#F%\"\"'" }}}{EXCHG {PARA 389 "> " 0 "" {MPLTEXT 1 0 25 "integra
te(sin_series, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG#\"\"\"\"
\"#\"\"##!\"\"\"#C\"\"%#F&\"$?(\"\"'-%\"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(powse
ries); #procedury, slouzici k praci s mocninnymi radami" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#77%(composeG%(evalpowG%(inverseG%*multconstG%)mu
ltiplyG%)negativeG%'powaddG%'powcosG%*powcreateG%(powdiffG%'powexpG%'p
owintG%'powlogG%(powpolyG%'powsinG%)powsolveG%(powsqrtG%)quotientG%*re
versionG%)subtractG%(tpsformG" }}}{EXCHG {PARA 393 "> " 0 "" {MPLTEXT 
1 0 23 "powcreate(f(n)=a^n/n!);" }}}{EXCHG {PARA 394 "> " 0 "" 
{MPLTEXT 1 0 36 "powcreate(g(n)=(-1)^(n+1)/n,g(0)=0);" }}}{EXCHG 
{PARA 395 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*$)%\"aG\"\"#\"\"\"#\"\"\"F'" }}}{EXCHG {PARA 396 "> \+
" 0 "" {MPLTEXT 1 0 25 "f_series:=tpsform(f,x,5);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%)f_seriesG+/%\"xG\"\"\"\"\"!%\"aG\"\"\",$*$)F)\"\"#\"
\"\"#F'F.\"\"#,$*$)F)\"\"$F/#F'\"\"'\"\"$,$*$)F)\"\"%F/#F'\"#C\"\"%-%
\"OG6#F'\"\"&" }}}{EXCHG {PARA 397 "> " 0 "" {MPLTEXT 1 0 25 "g_series
:=tpsform(g,x,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)g_seriesG+-%\"
xG\"\"\"\"\"\"#!\"\"\"\"#\"\"##F'\"\"$\"\"$#F*\"\"%\"\"%-%\"OG6#F'\"\"
&" }}}{EXCHG {PARA 398 "> " 0 "" {MPLTEXT 1 0 31 "s:=powadd(f,g): tpsf
orm(s,x,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\"\"\"\"\"!,&%\"
aGF%F%F%\"\"\",&*$)F(\"\"#\"\"\"#F%F-#!\"\"F-F%\"\"#-%\"OG6#F%\"\"$" }
}}{EXCHG {PARA 399 "> " 0 "" {MPLTEXT 1 0 33 "p:=multiply(f,g): tpsfor
m(p,x,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"xG\"\"\"\"\"\",&#!\"
\"\"\"#F%%\"aGF%\"\"#,(#F%\"\"$F%F+F(*$)F+F*\"\"\"#F%F*\"\"$-%\"OG6#F%
\"\"%" }}}{EXCHG {PARA 400 "> " 0 "" {MPLTEXT 1 0 30 "d:=powdiff(f): t
psform(d,x,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+-%\"xG%\"aG\"\"!*$)
F%\"\"#\"\"\"\"\"\",$*$)F%\"\"$F*#\"\"\"F)\"\"#,$*$)F%\"\"%F*#F1\"\"'
\"\"$-%\"OG6#F1\"\"%" }}}{EXCHG {PARA 401 "> " 0 "" {MPLTEXT 1 0 29 "i
:=powint(f): tpsform(i,x,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#++%\"x
G\"\"\"\"\"\",$%\"aG#F%\"\"#\"\"#,$*$)F(F*\"\"\"#F%\"\"'\"\"$-%\"OG6#F
%\"\"%" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "Vypocty limit" }}
{EXCHG {PARA 402 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 40 "Limit( cos(x)
^(1/x^3), x=0): %=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&Lim
itG6$)-%$cosG6#%\"xG*&\"\"\"F-*$)F+\"\"$F-!\"\"/F+\"\"!%*undefinedG" }
}}{EXCHG {PARA 403 "" 0 "" {TEXT -1 20 "Jednostranne limity:" }}{PARA 
404 "> " 0 "" {MPLTEXT 1 0 37 "Limit(cos(x)^(1/x^3), x=0, 'right'): " 
}}}{EXCHG {PARA 405 "> " 0 "" {MPLTEXT 1 0 11 "%=value(%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6%)-%$cosG6#%\"xG*&\"\"\"F-*$)F+\"
\"$F-!\"\"/F+\"\"!%&rightGF3" }}}{EXCHG {PARA 406 "> " 0 "" {MPLTEXT 
1 0 36 "Limit(cos(x)^(1/x^3), x=0, 'left'): " }}}{EXCHG {PARA 407 "> \+
" 0 "" {MPLTEXT 1 0 11 "%=value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/-%&LimitG6%)-%$cosG6#%\"xG*&\"\"\"F-*$)F+\"\"$F-!\"\"/F+\"\"!%%leftG
%)infinityG" }}}{EXCHG {PARA 408 "> " 0 "" {MPLTEXT 1 0 21 "y:=exp(a*x
)*cos(b*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG*&-%$expG6#*&%\"a
G\"\"\"%\"xGF+F+-%$cosG6#*&%\"bGF+F,\"\"\"F+" }}}{EXCHG {PARA 409 "> \+
" 0 "" {MPLTEXT 1 0 22 "limit(y, x=-infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%&limitG6$*&-%$expG6#*&%\"aG\"\"\"%\"xGF,F,-%$cosG6#*&
%\"bGF,F-\"\"\"F,/F-,$%)infinityG!\"\"" }}}{EXCHG {PARA 410 "> " 0 "" 
{MPLTEXT 1 0 12 "assume(a>0):" }}}{EXCHG {PARA 411 "> " 0 "" {MPLTEXT 
1 0 22 "limit(y, x=-infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"
!" }}}{EXCHG {PARA 412 "> " 0 "" {MPLTEXT 1 0 41 "expr:=(exp(x)-sum(x^
k/k!, k=0..11))/x^12;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%exprG*&,<-
%$expG6#%\"xG\"\"\"!\"\"F+F*F,*$)F*\"\"#\"\"\"#F,F/*$)F*\"\"$F0#F,\"\"
'*$)F*\"\"%F0#F,\"#C*$)F*\"\"&F0#F,\"$?\"*$)F*F6F0#F,\"$?(*$)F*\"\"(F0
#F,\"%S]*$)F*\"\")F0#F,\"&?.%*$)F*\"\"*F0#F,\"'!)GO*$)F*\"#5F0#F,\"(+)
GO*$)F*\"#6F0#F,\")+o\"*RF0*$)F*\"#7F0!\"\"" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 17 "limit(expr, x=0);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#-%&limitG6$*&,<-%$expG6#%\"xG\"\"\"!\"\"F,F+F-*$)F+\"\"#\"\"\"#F-F0
*$)F+\"\"$F1#F-\"\"'*$)F+\"\"%F1#F-\"#C*$)F+\"\"&F1#F-\"$?\"*$)F+F7F1#
F-\"$?(*$)F+\"\"(F1#F-\"%S]*$)F+\"\")F1#F-\"&?.%*$)F+\"\"*F1#F-\"'!)GO
*$)F+\"#5F1#F-\"(+)GO*$)F+\"#6F1#F-\")+o\"*RF1*$)F+\"#7F1!\"\"/F+\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Order:=13;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%&OrderG\"#8" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "limit(expr, x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
#\"\"\"\"*+;+z%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "Student Calculus Package" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 
414 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 415 "> \+
" 0 "" {MPLTEXT 1 0 17 "f:=x->-2/3*x^2+x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(,&*$)9$\"\"#\"
\"\"#!\"#\"\"$F/\"\"\"F(F(F(" }}}{EXCHG {PARA 416 "> " 0 "" {MPLTEXT 
1 0 16 "(f(x+h)-f(x))/h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$),&%
\"xG\"\"\"%\"hGF)\"\"#\"\"\"#!\"#\"\"$F*F)*$)F(F+F,#F+F/F,F*!\"\"" }}}
{EXCHG {PARA 417 "> " 0 "" {MPLTEXT 1 0 13 "Limit(%,h=0);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%&LimitG6$*&,(*$),&%\"xG\"\"\"%\"hGF,\"\"#\"\"
\"#!\"#\"\"$F-F,*$)F+F.F/#F.F2F/F-!\"\"/F-\"\"!" }}}{EXCHG {PARA 418 "
> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,&%\"xG#!\"%\"\"$\"\"\"F(" }}}{EXCHG {PARA 419 "> " 0 "" {MPLTEXT 1 0 
13 "eval(%, x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}
{EXCHG {PARA 420 "> " 0 "" {MPLTEXT 1 0 23 "showtangent(f(x), x=0);" }
}{PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6$7S7$$!#5\"\"!F(7$$!1nmm;p0k&
*!#:F,7$$!1LL$3<XZ=*F.F07$$!1mmmT%p\"e()F.F37$$!1nmm\"4m(G$)F.F67$$!1L
L$3i.9!zF.F97$$!1nm;/R=0vF.F<7$$!1,+]P8#\\4(F.F?7$$!1mm;/siqmF.FB7$$!1
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$$!1****\\P'psm\"F.F`o7$$!1****\\74_c7F.Fco7$$!1:LL$3x%z#)!#;Ffo7$$!1I
LL3s$QM%FhoFjo7$$!1^omm;zr)*!#=F]p7$$\"1WLLezw5VFhoFap7$$\"1.++v$Q#\\
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$\"1,+]i&p@[#F.F`q7$$\"1+++vgHKHF.Fcq7$$\"1lmmmZvOLF.Ffq7$$\"1,++]2goP
F.Fiq7$$\"1KL$eR<*fTF.F\\r7$$\"1-++])Hxe%F.F_r7$$\"1mm;H!o-*\\F.Fbr7$$
\"1,+]7k.6aF.Fer7$$\"1mmm;WTAeF.Fhr7$$\"1****\\i!*3`iF.F[s7$$\"1NLLL*z
ym'F.F^s7$$\"1OLL3N1#4(F.Fas7$$\"1pm;HYt7vF.Fds7$$\"1-+++xG**yF.Fgs7$$
\"1qmmT6KU$)F.Fjs7$$\"1OLLLbdQ()F.F]t7$$\"1++]i`1h\"*F.F`t7$$\"1-+]P?W
l&*F.Fct7$$\"#5F*Fft-%'COLOURG6&%$RGBG$Fgt!\"\"F*F*-F$6$7S7$F($!1mmmmm
mmw!#97$F,$!1nf,sY[aqFdu7$F0$!1#3$H2TWUlFdu7$F3$!1(eHa2>&*)fFdu7$F6$!1
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