Matematika - LS 24/25

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Nalezněte obecné řešení rovnice

y'y^{10}-\frac{1}{\cos^2 x}=0.

y=\sqrt[11]{10+\mathrm{tg} x+C}

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Žádná z předchozích odpovědí není správně.

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y=\sqrt[11]{11(\mathrm{tg} x+C)}

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y=\sqrt[9]{9(-\mathrm{tg} x+C)}

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y=\sqrt[11]{\frac{(\mathrm{tg} x+C)}{11}}

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Spočtěte \int_{7\pi}^{9\pi}\limits \sin \frac{x-3\pi}{2}\ \mathrm{d}x

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Určete Taylorův polynom druhého stupně funkce

f(x)=\cos(3x+\frac{\pi}{2})-2. se středem v bodě a=-\frac{\pi}{4}.

-2+\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x-\frac{\pi}{4})+\frac{9\sqrt 2}{2}(x-\frac{\pi}{4})^2

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-2+\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})+\frac{9\sqrt 2}{4}(x+\frac{\pi}{4})^2

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-2+\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})-\frac{9\sqrt 2}{2}(x+\frac{\pi}{4})^2

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-2+\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})+\frac{9\sqrt 2}{2}(x+\frac{\pi}{4})^2

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-2+\frac{\sqrt 2}{2}+\frac{\sqrt 2}{2}(x+\frac{\pi}{4})+\frac{\sqrt 2}{4}(x+\frac{\pi}{4})^2

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-2+\frac{\sqrt 2}{2}+\frac{3\sqrt 2}{2}(x+\frac{\pi}{4})-\frac{9\sqrt 2}{4}(x+\frac{\pi}{4})^2

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Spočtěte neurčitý integrál

\displaystyle\int\left(\frac{1}{x^{5}}+e\right)dx.

\displaystyle\frac{-1}{4x^{4}}+e^x+C

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\displaystyle\ln\left|x^{5}\right|+ex+C

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\displaystyle\frac{-1}{4x^{4}}+ex+C

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\displaystyle\frac{6}{x^{6}}+ex+C

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\displaystyle\frac{6}{x^{6}}+e^x+C

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\displaystyle\ln\left|x^{5}\right|+e^x+C

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Určete Taylorův polynom druhého stupně funkce

f(x)=\sin(5x-\frac{\pi}{6})+7. se středem v bodě a=\frac{\pi}{6}.

7+\frac{\sqrt 3}{2}-\frac{5}{2}(x-\frac{\pi}{6})+\frac{25\sqrt 3}{4}(x-\frac{\pi}{6})^2

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\frac{13}{2}-\frac{5\sqrt 3}{2}(x-\frac{\pi}{6})-\frac{25}{4}(x-\frac{\pi}{6})^2

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7+\frac{\sqrt 3}{2}-\frac{1}{2}(x-\frac{\pi}{6})-\frac{\sqrt 3}{4}(x-\frac{\pi}{6})^2

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7+\frac{\sqrt 3}{2}-\frac{5}{2}(x+\frac{\pi}{6})-\frac{25\sqrt 3}{2}(x+\frac{\pi}{6})^2

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7+\frac{\sqrt 3}{2}-\frac{5}{2}(x-\frac{\pi}{6})-\frac{25\sqrt 3}{2}(x-\frac{\pi}{6})^2

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7+\frac{\sqrt 3}{2}-\frac{5}{2}(x-\frac{\pi}{6})-\frac{25\sqrt 3}{4}(x-\frac{\pi}{6})^2

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Spočtěte \int_{-5\pi}^{-4\pi}\limits \sin \frac{2x+5\pi}{3}\ \mathrm{d}x

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