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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT 257 6 "MB001c" }}{PARA 256 "" 0 "" {TEXT 256 40 "Matematick\341 \+
anal\375za II - cvi\350en\355 s Maple" }}{PARA 256 "" 0 "" {TEXT 258 
10 "4. semin\341\370" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 259 1 " " }
{TEXT -1 33 "Diferenci\341l funkce jedn\351 prom\354nn\351" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 21 "Definice diferenci\341lu" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "df := (x0, h) -> D(f)(x0)*h;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT 260 8 "P\370\355klad\n" }{TEXT -1 49 "Pomoc\355 diferenc
i\341lu spo\350t\354te p\370ibli\236n\354 arctg 0.97" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 297 "Funkci arctg nahrad\355me ve zvolen\351m bod
\354 x0 te\350nou a spo\350te funk\350n\355ho hodnotu v bod\354 x=0.97
, co\236 je p\370ibli\236n\341 funk\350n\355 hodnota funkce arctg.\nBo
d x0 zvol\355me v bl\355zk\351m okol\355 bodu x (p\370i ru\350n\355m p
o\350\355t\341n\355 v\236dy bod, jeho\236 funk\350n\355 hodnotu zn\341
me \350i jednodu\232e z\355sk\341me), t\355m dos\341hneme v\354t\232
\355 p\370esnosti v\375po\350tu." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
25 "Nadefinujeme funkci arctg" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f \+
:= x -> arctan(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x:=0.9
7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x0:=1;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "h:=x-x0;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 31 "Spo\350teme diferenci\341l v bod\354 x0 " }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "df(x0, h);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "fh_dif:=f(x0) + df(x0, h);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 43 "V\375po\350et funk\350n\355 hodnoty pomoc\355 direfenci
\341lu" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fh_dif:=evalf(%);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "V\375po\350et p\370\355m\375m dosa
zen\355m" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fh_primo:=evalf(f(x));
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Odchylka v\375po\350tu" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "odchylka:=abs(fh_dif - fh_primo);" 
}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "\332lohy k vypracov\341n\355" 
}}{EXCHG {PARA 15 "" 0 "" {TEXT -1 39 "Pomoc\355 diferenci\341lu spo
\350t\354te p\370ibli\236n\354 " }{XPPEDIT 18 0 "sqrt(28)" "6#-%%sqrtG
6#\"#G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 1 " " }{TEXT 261 30 "Tayl
or\371v a Maclaurin\371v polynom" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
160 "Taylorova aproximace = rozvoj funkce do mocninn\351 \370adou v ok
ol\355 bodu x0\nV na\232em p\370\355pad\354 budeme uva\236ovat v\236dy
 kone\350n\351 \370ady, tz. rozvoj funkce Taylorov\375m polynomem" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 262 8 "P\370\355klad\n" }{TEXT -1 45 "Vyp
o\350t\354te Taylorov\371v polynom stupn\354 3 funkce " }{XPPEDIT 18 
0 "exp(x^2)" "6#-%$expG6#*$%\"xG\"\"#" }{TEXT -1 8 " v bod\354 " }
{XPPEDIT 18 0 "x=1" "6#/%\"xG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "f:=x->exp(x^2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
39 "Prvn\355, druh\341 a t\370et\355 dderivace funkce f" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 51 "d[1]:=(D@@1)(f);\nd[2]:=(D@@2)(f);\nd[3]:=(D@@
3)(f);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "T[3]:=f(1)+d[1]
(1)*(x-1)+d[2](1)*(x-1)^2/(2!)+d[3](1)*(x-1)^3/(3!);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 76 "Maple obsahuje \370adu procedur a funkc\355 pr
\341v\354 pro pr\341ci Taylorov\375mi polynomy. " }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 7 "Funkce " }{HYPERLNK 17 "taylor" 2 "taylor" "" }
{TEXT -1 27 " po\350\355t\341 Taylorovy polynomy." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 26 "TP[3]:=taylor(f(x),x=1,4);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 34 "V\375sledek je typu series. P\370\355kazem " }
{HYPERLNK 17 "convert" 2 "convert" "" }{TEXT -1 25 " jej p\370evedeme \+
na polynom" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "TP[3]:=conver
t(%, polynom);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Uveden\375 post
up lze jednodu\232e zobecnit " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 56 "t:=(f, x0, n) -> sum((D@@i)(f)(x0)/i!*(x-x0)^i, i=0..n);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 263 8 "P\370\355klad\n" }{TEXT -1 85 "S v
yu\236it\355m zobecn\354n\351 funkce vypo\350t\354te Taylorovy polynom
y v bod\354 1 stupn\354 1..5 funkce " }{XPPEDIT 18 0 "sqrt(1+1/x)" "6#
-%%sqrtG6#,&\"\"\"F'*&F'F'%\"xG!\"\"F'" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f:=x -> sqr
t(1+1/x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "seq(print(t(f,
 1, j)), j=1..5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Grafy t\354c
hto polynom\371 zobraz\355me v jednom obr\341zku" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "plot([seq(t(f, 1, j), j=1..5)], x=-5..5, -10..10);" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "K vizualizaci graf\371 Taylorov
\375ch polynom\371 slou\236\355 procedura " }{HYPERLNK 17 "TaylorAppro
ximation" 2 "Student[Calculus1][TaylorApproximation]" "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(Student[Calculus1]):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "TaylorApproximation(f(x), x=
1, order=1..20, view = [-5..5, -10..10], output = animation);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "\332lohy k vypracov\341n\355" }}
{EXCHG {PARA 15 "" 0 "" {TEXT -1 61 "Vytvo\370te animaci Maclaurinov
\375ch polynom\371 stupn\354 1..10 funkce " }{XPPEDIT 18 0 "(8-x^3)^(1
/3)" "6#),&\"\")\"\"\"*$%\"xG\"\"$!\"\"*&F&F&F)F*" }}{PARA 0 "" 0 "" 
{TEXT -1 32 "    \330e\232t\354 bez pou\236it\355 procedury " }
{HYPERLNK 17 "TaylorApproximation" 2 "Student[Calculus1][TaylorApproxi
mation]" "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 27 " M\355sto p
ro Va\232e experimenty" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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