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Matematika - LS 24/25

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Spočtěte hodnotu f ' (1), když f(x)=x^3+2x^2+8x-3f(x)=x^3+2x^2+8x-3
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Určete definiční obor funkce

f(x)=\textrm{arcsin}(\frac{x}{6}-3).f(x)=\textrm{arcsin}(\frac{x}{6}-3).
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Určete definiční obor funkce

f(x)=\sqrt[4]{\frac{x+7}{6-6x}}+\sqrt[4]{6}.f(x)=\sqrt[4]{\frac{x+7}{6-6x}}+\sqrt[4]{6}.
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Nalezněte definiční obor funkce dané předpisem f(x)=\sqrt{-x^2+2x+15}.f(x)=\sqrt{-x^2+2x+15}.

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Vyřešte nerovnici

\frac{-8x-8}{4x-8}> -1.\frac{-8x-8}{4x-8}> -1.
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Vyřešte nerovnici

-2x^2-2x-12\leq-7.-2x^2-2x-12\leq-7.
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Vypočtěte nejmenší reálné číslo, které je řešením soustavy nerovnic

9 ≤ 18 - 5x ≤ 12. Zaokrouhlete na dvě desetinná místa.

 

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Určete definiční obor funkce

f(x)=\log(x^2+3x-10)+2\sqrt{5-x}.f(x)=\log(x^2+3x-10)+2\sqrt{5-x}.
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Určete definiční obor funkce f(x)=log(x²-4x+3)-(-6-x)½.
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Určete definiční obor funkce

f(x)=\log\frac{8x+40}{x-6}+3\sqrt{4-x}.f(x)=\log\frac{8x+40}{x-6}+3\sqrt{4-x}.
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