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{SECT 0 {EXCHG {PARA 265 "" 0 "" {TEXT 302 35 "Matematick\351 v\375po
\350ty se syst\351m Maple" }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 77 "au
tor:  Ing. Vladim\355r \216\341k\n  email:  zakyn@centrum.cz\n        \+
         web:   " }{URLLINK 17 "www.vladimirzak.com/maple" 4 "www.vlad
imirzak.com/maple" "" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "
" 0 "" {TEXT -1 12 "            " }{TEXT 300 9 "recenzent" }{TEXT -1 
3 ":  " }{TEXT 299 31 "Prof. RNDr. Ji\370\355 H\370eb\355\350ek, CSc.
" }}{PARA 265 "" 0 "" {TEXT -1 48 "CENTRUM BIOSTATISTIKY A ANAL\335Z (
CBA LF a P\370F MU)" }}{PARA 265 "" 0 "" {TEXT -1 43 "L\351ka\370sk
\341 a P\370\355rodov\354deck\341 fakulta MU v Brn\354" }}{PARA 265 "
" 0 "" {TEXT -1 20 "hrebicek@cba.muni.cz" }}{PARA 265 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 265 "" 0 "" {TEXT -1 478 "Tento dokument je ur
\350en jen pro v\375ukov\351 \372\350ely a pro pou\236it\355 jen osoba
mi, kter\375m byl tento dokument poskytnut p\370\355mo autorem, pop
\370. si ho st\341hli z webov\351ho s\355dla autora. Jak\351koliv \350
\341sti dokumentu nen\355 mo\236n\351 pou\236\355t bez citace zdoje, t
edy n\341zvu dokumentu a jm\351na autora s kontaktn\355mi informacemi \+
(jak je zobrazeno v hlavi\350ce), kter\341 mus\355 b\375t autorovi sd
\354lena. Pro jin\351 pou\236it\355 ne\236 pro osobn\355 pot\370eby os
ob, tedy pro distribuci \350i kop\355rov\341n\355, je nutn\351 obdr
\236et p\355semn\375 souhlas autora. " }}{PARA 265 "" 0 "" {TEXT -1 0 
"" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }{TEXT 301 59 "Soubor vznikl s po
dporou grantov\351ho projektu FRV\212 3323/2006" }{TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 16 "Spojitost
 funkce" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "V tomto odstavci se bud
eme zab\375vat singularitami funkce. D\371le\236itost vyplyne z cel
\351ho odstavce." }}{PARA 0 "" 0 "" {TEXT -1 60 "Nejprve uve\357me def
inici jednotliv\375ch typ\371 bod\371 nespojitosti." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 288 9 "Definice:" }}{PARA 0 "
" 0 "" {TEXT -1 13 "Nech\235 funkce " }{TEXT 289 1 "f" }{TEXT -1 30 " \+
je definov\341na v jist\351m okol\355 " }{OLE 1 4611 1 "[xm]Br=WfoRrB:
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:::::::::::::::::::::::::::::::::::::3:" }{TEXT -1 1 " " }}{PARA 16 "
" 0 "" {TEXT 285 26 "odstranitelnou singularitu" }{TEXT -1 20 ", jestl
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:::vyyuy:>:<:::::::::::::::::::vYxI:;Z::::::::::::::::::::yay=J:B:::::
:::3:" }{TEXT -1 16 " nen\355 definov\341no" }}{PARA 16 "" 0 "" {TEXT 
286 20 "nespojitost 1. druhu" }{TEXT -1 48 " (typu skoku), jestli\236e
 existuj\355 vlastn\355 limity " }{OLE 1 4608 1 "[xm]Br=WfoRrB:::wk;ny
yI;G:;:j::>:B>N:F:nyyyyy]::yyyyyy:::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::fyyyyyq:nY^:f:v:nYnyyyYyA:::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ND
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@j:j;<J:vYxY:B::::::F:;jnJ:J;vCS=[LsfFaMR>@>Z::::::::kJ;@jysyC:yayA:<:
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:::::::::::::j:b:<Z::::::::::j:nyyYZDjysyAbm?:;JZC:bKg:UTRcETcTX[US;SG
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jEJJmjCB:Gc;YJHvyyuy;B:UD:[Z:>ryMMyyyyYjlZ:nj<B:QB:n>^;UTRZ_?Z:>PEZ:F[
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CJC;V:qZF:KN:<Z;r<b>?SE@j:N;nFNjbJ:HRvN:?VD<Z<V[:>:G;Sjysy=Z:>:^=<jw?<
IZ:>:sg:bu=b:?bBaTXaEWEUU>Z:N[:F>OV:<Z:FZ:>:ccs_jVAv]YQ<>Z:f?=J<Jr?:AB
:;B:;:::Ja@Na`><::::^=NZ:F];yi;JJ`XC<J:>:SB:GOv]XCfZ;:Z:::::fB]mtFFcmn
vGWMJ<Ja<jj:gmlB:;:::::JJ<J;vyyuy:>:;B::::::v<Vm;B:;B::::::::::::jysy:
>:<:::::::::::::::::::vYxI:;Z::::::::::::::::::::yay=J:B::::::::^dcSSZ
ZjpnGZ\\CUrJ:J::E<==v?ZnA<I\\JOXBweZ:RK:B>H^;kAQ^dZID:<[:kZxQ^>\\IFBvE
xo\\RJj:<j:DZ<NZ:j:F:Aj:^:dj:<j;v<b:?:Njc;U]EJ;<j;K<NLrZV:qZFF:?J>C:=R
:;r<rDh\\;J?rZG=?FD>Z=@I?J;a\\<JPjEJ:N:Zc;U=B:A>CJC;V:qZF:KN:<Z;r<b>:O
:G=?FD>Z=@I?J;a\\:B::::::::::::::::::::::::::::3:" }{TEXT -1 13 " a js
ou r\371zn\351" }}{PARA 16 "" 0 "" {TEXT 287 20 "nespojitost 2. druhu
" }{TEXT -1 79 ", jestli\236e alespo\362 jedna z jednostrann\375ch lim
it neexistuje nebo je nevlastn\355   " }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "Pro h
led\341n\355 bod\371  nespojitosti lze v Maplu u\236\355t n\354kolik p
\370\355kaz\371" }}{PARA 15 "" 0 "" {TEXT 265 21 "discont(fce(x),x)   \+
 " }{TEXT -1 67 "      \n-  v\375sledkem je mno\236ina bod\371 v nich
\236 m\371\236e nespojitost nastat" }}{PARA 15 "" 0 "" {TEXT 266 58 "f
discont(fce(x), x=interval, p\370esnost, pou\236it\341 metoda )   " }
{TEXT -1 74 "  \n- numerick\351 hled\341n\355 nespojitost\355 funkce, \+
m\341 velk\341 omezen\355 -v\355ce v HELPU" }}{PARA 15 "" 0 "" {TEXT 
267 35 "iscont( f(x), x=a..b, 'interval' ) " }{TEXT -1 23 "\n- tento p
\370\355kaz vyp\355\232e " }{TEXT 272 4 "true" }{TEXT -1 90 ", v p\370
\355pad\354, \236e v dan\351m intervalu nenalezl \236\341dn\375 \"pode
z\370el\375\" bod v opa\350n\351m p\370\355pad\354 vyp\355\232e " }
{TEXT 269 5 "false" }{TEXT -1 46 ". T\370et\355 parametr je nepovinn
\375, nab\375v\341 hodnoty " }{TEXT 270 4 "open" }{TEXT -1 3 " / " }
{TEXT 271 6 "closed" }{TEXT -1 47 ", pro otev\370en\375 / uzav\370en
\375 interval, implicitn\354 " }{TEXT 261 4 "open" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 140 "V p\370\355pad\354, hled\341n\355 singul
\341rn\355ch bod\371 funkc\355 v\355ce prom\354nn\375ch nem\371\236eme
 u\236\355t ani jeden z p\370edchoz\355ch p\370\355kaz\371. Je nutn
\351 pou\236\355t n\354kter\375 z p\370\355kaz\371" }}{PARA 15 "" 0 "
" {TEXT 268 75 "singular( f(x) , x )\nsingular( f(x,y), \{x,y\})\nsing
ular( f(x,y,z), \{x,y,z\})\n" }{TEXT -1 39 "- je zalo\236en na v\375po
\350tu pomoc\355 p\370\355kazu " }{TEXT 262 5 "solve" }{TEXT -1 40 ", \+
tj. m\341 ur\350it\351 omezen\355 (viz. P\370\355klad 1)" }}{PARA 257 
"" 0 "" {TEXT -1 0 "" }{TEXT 277 0 "" }{TEXT 278 13 "M\355sto funkce \+
" }{TEXT 279 4 "f(x)" }{TEXT 280 52 " lze pou\236\355t i v\375raz pro \+
v\375po\350et hodnoty t\351to funkce." }}{PARA 257 "" 0 "" {TEXT 276 
75 "Podrobnosti a p\370\355klady k t\354mto p\370\355kaz\371m naleznet
e v n\341pov\354d\354 syst\351mu Maple." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart:" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "P\370
\355klad 1" }}{EXCHG {PARA 0 "" 0 "" {TEXT 260 25 "Odstraniteln\341 si
ngularita" }{TEXT -1 29 " - probl\351m p\370i \370e\232en\355 rovnice
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(x-1)^3/(x^2-1)=0;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&,&%\"xG\"\"\"F'!\"\"\"\"$,&*$)F&\"
\"#F'F'F'F(F(\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=lh
s(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&,&%\"xG\"\"\"F(!\"\"
\"\"$,&*$)F'\"\"#F(F(F(F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "
\330e\232\355me rovnici pomoc\355 " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "solve(\{f\},x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<#
/%\"xG\"\"\"F#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Vid\355me, \236
e \370e\232en\355m je bod " }{TEXT 256 3 "x=1" }{TEXT -1 64 ", ale pok
us o dosazen\355 \370e\232en\355 sel\236e, proto\236e bychom d\354lili
 nulou" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "subs(%,f);" }}
{PARA 8 "" 1 "" {TEXT -1 43 "Error, numeric exception: division by zer
o\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "D\371vodem tohoto chov\341
n\355 je odstraniteln\341 singularita v bod\354 " }{TEXT 257 3 "x=1" }
{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(f,x=
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