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Matematika - LS 24/25

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Nalezněte asymptoty grafu y= \frac{-7x^3+9}{4x^2-9}y= \frac{-7x^3+9}{4x^2-9}.
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Vypočtěte směrnici tečny ke grafu funkce f(x)=5\cdot\ln( { 4x^2+4x+4})f(x)=5\cdot\ln( { 4x^2+4x+4}) v bodě T=[4,?].T=[4,?]. Zaokrouhlete na dvě desetinná místa.

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Spočtěte limitu

\displaystyle\lim_{x\to 10}\frac{x^2-20x+100}{x^2-16x+60}\displaystyle\lim_{x\to 10}\frac{x^2-20x+100}{x^2-16x+60}
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Určete maximální intervaly monotonie funkce

f:y=e^x(-2x-6)f:y=e^x(-2x-6).
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Spočtěte absolutní minimum (nejmenší funkční hodnotu) funkce f(x)=2x^3+5x^2+5f(x)=2x^3+5x^2+5 pro x\in\langle -5,5\ranglex\in\langle -5,5\rangle.

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Určete, ve kterém bodě má funkce y=4x^3+12x^2-36x+4y=4x^3+12x^2-36x+4 lokální maximum.
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Jaká musí být hodnota čísla q, aby přímka -10x+y+q=0 byla tečnou grafu y=-x²+4x-2?
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Nalezněte asymptoty grafu y= \frac{7-5x^2}{1+9x^2}y= \frac{7-5x^2}{1+9x^2}.
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Spočtěte limitu

\displaystyle\lim_{x\to -6}\frac{x^2+16x+60}{x^2+11x+30}\displaystyle\lim_{x\to -6}\frac{x^2+16x+60}{x^2+11x+30}
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Spočtěte limitu \displaystyle\lim_{x\to\infty} \frac{5x^2+5x+4}{4x^2+8x+12}\displaystyle\lim_{x\to\infty} \frac{5x^2+5x+4}{4x^2+8x+12}

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