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Matematika - LS 24/25

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Nalezněte asymptoty grafu y= \frac{x^2-3x-4}{3x-9}y= \frac{x^2-3x-4}{3x-9}.
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Spočtěte limitu \displaystyle\lim_{x\to\infty} \frac{8x^2+2x+19}{4x^2+3x+18}\displaystyle\lim_{x\to\infty} \frac{8x^2+2x+19}{4x^2+3x+18}

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Spočtěte limitu

\displaystyle\lim_{x\to -1}\frac{x^2+2x+1}{x^2+10x+9}\displaystyle\lim_{x\to -1}\frac{x^2+2x+1}{x^2+10x+9}
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Jaká musí být hodnota čísla q, aby přímka x+2y+q=0 byla normálou grafu y=x²-4x-6?
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Určete definiční obor funkce

f(x)=\textrm{arcsin}(\frac{x}{4}-5).f(x)=\textrm{arcsin}(\frac{x}{4}-5).
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Nalezněte definiční obor funkce dané předpisem f(x)=\sqrt{-x^2+5x+6}.f(x)=\sqrt{-x^2+5x+6}.

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Určete definiční obor funkce

f(x)=\ln(\frac{x+9}{3-3x})+\ln(2).f(x)=\ln(\frac{x+9}{3-3x})+\ln(2).
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Spočtěte hodnotu f ' (2), když f(x)=x^3+3x^2-8x-8f(x)=x^3+3x^2-8x-8
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Spočtěte hodnotu f ' (-3), když f(x)=(2x-3)/(x-2).

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Spočtěte derivaci dané funkce

f(x)=\frac{4x^2+2}{e^{8x}}.f(x)=\frac{4x^2+2}{e^{8x}}.
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