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Matematika - LS 24/25

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Spočtěte limitu

\displaystyle\lim_{x\to -6}\frac{x^2+4x-12}{x^2+14x+48}\displaystyle\lim_{x\to -6}\frac{x^2+4x-12}{x^2+14x+48}
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Spočtěte derivaci dané funkce

f(x)=x\cdot\frac{2x-3}{4x-9}.f(x)=x\cdot\frac{2x-3}{4x-9}.
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Spočtěte f ' (-5), když f(x)=(4x²-8)/(x-3).

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Na vhodném intervalu zderivujte funkci f(x)=\frac{1}{x^5}-\ln{7}.f(x)=\frac{1}{x^5}-\ln{7}.
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Spočtěte hodnotu f ' (-2), když f(x)=x^3+3x^2+4x+7f(x)=x^3+3x^2+4x+7
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Určete definiční obor funkce

f(x)=\textrm{arccos}(\frac{x}{8}+3).f(x)=\textrm{arccos}(\frac{x}{8}+3).
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Nalezněte definiční obor funkce dané předpisem f(x)=\sqrt{x^2+6x+8}.f(x)=\sqrt{x^2+6x+8}.

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Určete definiční obor funkce

f(x)=\ln(\frac{-3x+9}{5-5x})+\ln(8).f(x)=\ln(\frac{-3x+9}{5-5x})+\ln(8).
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Vyřešte nerovnici

\frac{-3x-6}{2x-8}\geq -1.\frac{-3x-6}{2x-8}\geq -1.
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Vyřešte nerovnici

4x^2-24x+30 < -2.4x^2-24x+30 < -2.
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