Matematika - LS 24/25

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Spočtěte neurčitý integrál

\displaystyle\int\left(\frac{1}{x^{8}}+e\right)dx.

\displaystyle\ln\left|x^{8}\right|+e^x+C

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\displaystyle\ln\left|x^{8}\right|+ex+C

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\displaystyle\frac{9}{x^{9}}+e^x+C

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\displaystyle\frac{9}{x^{9}}+ex+C

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\displaystyle\frac{-1}{7x^{7}}+e^x+C

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\displaystyle\frac{-1}{7x^{7}}+ex+C

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Určete Taylorův polynom druhého stupně funkce

f(x)=\sin(5x-\pi)-3. se středem v bodě a=\frac{\pi}{4}.

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

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

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

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

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

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Spočtěte \int_{-8\pi}^{-7\pi}\limits \cos \frac{2x+3\pi}{6}\ \mathrm{d}x

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Nalezněte obecné řešení rovnice

y'y^{9}-\frac{1}{\cos^2 x}=0.

y=\sqrt[10]{9+\mathrm{tg} x+C}

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

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y=\sqrt[8]{8(-\mathrm{tg} x+C)}

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y=\sqrt[10]{\frac{(\mathrm{tg} x+C)}{10}}

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Žádná z předchozích odpovědí není správně.

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Určete obsah rovinného obrazce ohraničeného křivkami 3x-2y=0 a y=\frac{x^{2}}{2}+2x-1.

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Určete Taylorův polynom druhého stupně funkce

f(x)=\sin(5x-\pi)+7. se středem v bodě a=\frac{\pi}{3}.

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

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

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

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

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

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

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