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pro ",
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 " a uka\[ZHacek]te, \[ZHacek]e \[RHacek]e\[SHacek]en\[IAcute] vyhovuje \
rovnic\[IAcute]m. Mo\[ZHacek]n\[EAcute] \[RHacek]e\[SHacek]en\[IAcute] je \
substituce pomoc\[IAcute] substitu\[CHacek]n\[IAcute]ho pravidla do \
p\[URing]vodn\[IAcute]ch rovnic a uk\[AAcute]zat, \[ZHacek]e v\[YAcute]sledek \
je True. "
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Cell["\<\
Vyhodno\[THacek]te n\[AAcute]sleduj\[IAcute]c\[IAcute] vstup, kter\[YAcute] \
definuje jednoduchou racion\[AAcute]ln\[IAcute] funkci. Racion\[AAcute]ln\
\[IAcute] funkce je takov\[AAcute], kter\[AAcute] v \[CHacek]itateli a \
jmenovateli obsahuje polynom. P\[RHacek]eve\[DHacek]te funkci na \
v\[YAcute]raz se spole\[CHacek]n\[YAcute]m jmenovatelem.\
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Cell[TextData[{
 "Pou\[ZHacek]ij funkci ",
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 " z odpov\[IAcute]daj\[IAcute]c\[IAcute]mi p\[RHacek]edpoklady a \
uka\[ZHacek]te, \[ZHacek]e n\[AAcute]sleduj\[IAcute]c\[IAcute] v\[YAcute]raz \
je 0 pokud ",
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Cell[TextData[{
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\[AAcute]cen bez pou\[ZHacek]it\[IAcute] ",
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Cell["\<\
Jedn\[IAcute]m ze zp\[URing]sob\[URing] kontroly symbolick\[YAcute]ch v\
\[YAcute]po\[CHacek]t\[URing] je substituce symbolick\[YAcute]ch \
v\[YAcute]raz\[URing] \[CHacek]\[IAcute]seln\[YAcute]mi hodnotami a proveden\
\[IAcute] stejn\[EAcute]ho v\[YAcute]po\[CHacek]tu \[CHacek]\[IAcute]seln\
\[EHacek].\
\>", "Text",
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Cell[TextData[{
 "Nap\[RHacek]\[IAcute]klad, vyhodno\[THacek]te n\[AAcute]sleduj\[IAcute]c\
\[IAcute] vstup, aby jste obdr\[ZHacek]eli v\[YAcute]sledek integrace z\
\[AAcute]visl\[YAcute] na parametru ",
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Cell[TextData[{
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\[CHacek]\[IAcute]seln\[EHacek] pomoc\[IAcute] funkce ",
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\[CHacek]\[IAcute]seln\[AAcute] hodnota. Sp\[IAcute]\[SHacek]e ne\[ZHacek] \
zad\[AAcute]vat jednu hodnotu argumentu na vstup je vhodn\[EHacek]j\[SHacek]\
\[IAcute] pou\[ZHacek]\[IAcute]t p\[RHacek]\[IAcute]stup, p\[RHacek]i kter\
\[EAcute]m je mo\[ZHacek]n\[EAcute] zadat v\[IAcute]ce hodnot parametru \
najednou. "
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Cell[TextData[{
 "Vyhodno\[THacek]te n\[AAcute]sleduj\[IAcute]c\[IAcute] vstup a \
obdr\[ZHacek]\[IAcute]te hodnotu integr\[AAcute]lu pro hodnotu ",
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 " rovnou 3. Hodnota parametru ",
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 " je zad\[AAcute]na pomoc\[IAcute]  ",
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Cell[TextData[{
 "Vyhodno\[THacek]te n\[AAcute]sleduj\[IAcute]c\[IAcute] vstup a \
ur\[CHacek]ete \[CHacek]\[IAcute]selnou aproximaci symbolick\[EAcute]ho v\
\[YAcute]sledku pro stejnou hodnotu ",
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 ". Srovnejte v\[YAcute]sledek s v\[YAcute]stupem \[CHacek]\[IAcute]seln\
\[EAcute] integrace z p\[RHacek]edch\[AAcute]zej\[IAcute]c\[IAcute]ho. "
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Cell[TextData[{
 "Tyto dva v\[YAcute]po\[CHacek]ty (\[CHacek]\[IAcute]seln\[AAcute] integrace \
pomoc\[IAcute] ",
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  ButtonBox["Integrate",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Integrate"]], "InlineFormula"],
 ") m\[URing]\[ZHacek]eme zkombinovat do jednoho v\[YAcute]sledku, kter\
\[YAcute] vr\[AAcute]t\[IAcute] ob\[EHacek] \[RHacek]e\[SHacek]en\[IAcute]."
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Cell[TextData[{
 "Vyhodnott\[EAcute] n\[AAcute]sleduj\[IAcute]c\[IAcute] vstup a srovnejte v\
\[YAcute]stup z funkce ",
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 " v\[YAcute]stup z funkce ",
 Cell[BoxData[
  ButtonBox["NIntegrate",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/NIntegrate"]], "InlineFormula"],
 ". "
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Cell[TextData[{
 "Pou\[ZHacek]ijte popsanou strategii ke kontrole n\[AAcute]sleduj\[IAcute]c\
\[IAcute]ho v\[YAcute]stupu funkce ",
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symbolick\[EAcute] parametry ",
 StyleBox["b", "MR"],
 " a ",
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 "."
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Cell[TextData[{
 "Pou\[ZHacek]ijte funkci Manipulate pro nastaven\[IAcute] r\[URing]zn\
\[YAcute]ch hodnot parametr\[URing] b a x1.\n\n",
 StyleBox["\[CapitalRHacek]e\[SHacek]en\[IAcute] line\[AAcute]rn\[IAcute]ch \
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Cell[TextData[{
 "Vyhodno\[THacek]te n\[AAcute]sleduj\[IAcute]c\[IAcute] dva vstupy a \
zkonstruujte mno\[ZHacek]inu line\[AAcute]rn\[IAcute]ch rovnic \
prom\[EHacek]nn\[YAcute]ch ",
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 ", ",
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 ", a ",
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 ", a druh\[YAcute] v\[YAcute]raz pou\[ZHacek]ijte tyto koeficienty ke \
konstrukci rovnic."
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Cell[TextData[{
 "Uka\[ZHacek]te \[RHacek]e\[SHacek]en\[IAcute] t\[EHacek]chto rovnic s pou\
\[ZHacek]it\[IAcute]m funkce ",
 Cell[BoxData[
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Cell[TextData[{
 "Nyn\[IAcute] \[RHacek]e\[SHacek]te stejnou soustavu rovnic pomoc\[IAcute] \
funkce ",
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  ButtonBox["LinearSolve",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/LinearSolve"]], "InlineFormula"],
 ". na rozd\[IAcute]l od funkce ",
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   BaseStyle->"Link",
   ButtonData->"paclet:ref/Solve"]], "InlineFormula"],
 ", ve kter\[EAcute] jsou argumenty rovnice, argumenty funkce ",
 Cell[BoxData[
  ButtonBox["LinearSolve",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/LinearSolve"]], "InlineFormula"],
 " jsou koeficienty rovnice.. V\[YAcute]sledek je tak\[EAcute] vr\[AAcute]cen \
v odli\[SHacek]n\[EAcute] form\[EHacek]. "
}], "Exercise",
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Cell[BoxData[""], "NonPrintButton",
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Cell[TextData[StyleBox["Pr\[AAcute]ce s \[RHacek]adami rozvoje \
funkc\[IAcute]", "Subsection"]], "ExerciseHeading",
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Cell[TextData[{
 "Vyhodno\[THacek]te n\[AAcute]sleduj\[IAcute]c\[IAcute] t\[RHacek]i vstupy, \
kter\[EAcute] generuj\[IAcute] rozvoj funkce ",
 Cell[BoxData[
  RowBox[{"Cos", "[", "x", "]"}]]],
 " do stupn\[EHacek] to 10 v okol\[IAcute] 0 a nakresl\[IAcute] graf, kter\
\[YAcute] srovn\[AAcute]v\[AAcute] tento polynomi\[AAcute]ln\[IAcute] rozvoj \
a vlastn\[IAcute] funkci ",
 Cell[BoxData[
  RowBox[{"Cos", "[", "x", "]"}]]],
 ". Jak\[YAcute] efekt m\[AAcute] pou\[ZHacek]it\[IAcute] funkce ",
 Cell[BoxData[
  ButtonBox["Normal",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Normal"]], "InlineFormula"],
 " ve v\[YAcute]po\[CHacek]tu? Co se stane, pokud aplikaci funkce ",
 Cell[BoxData[
  ButtonBox["Normal",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Normal"]], "InlineFormula"],
 " vynech\[AAcute]me? Pro\[CHacek]?"
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*)

(* End of internal cache information *)