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Matematika - LS 24/25

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Jaká musí být hodnota čísla q, aby přímka -x+y+q=0 byla tečnou grafu y=-3x²-5x+1?
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Vypočtěte směrnici tečny ke grafu funkce f(x)=\sqrt { x^2-7x+7}f(x)=\sqrt { x^2-7x+7} v bodě T=[-7,?].T=[-7,?]. Zaokrouhlete na dvě desetinná místa.

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Nalezněte asymptoty grafu y= \frac{-9x^2}{9x^2-1}y= \frac{-9x^2}{9x^2-1}.
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Spočtěte limitu \displaystyle\lim_{x\to-\infty} \frac{9x^2+6x+9}{4x^2+8x+9}\displaystyle\lim_{x\to-\infty} \frac{9x^2+6x+9}{4x^2+8x+9}

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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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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 f ' (-5), když f(x)=(4x²-8)/(x-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)=\textrm{arccos}(\frac{x}{8}+3).f(x)=\textrm{arccos}(\frac{x}{8}+3).
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