Matematika - LS 24/25

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Spočtěte \int_{-7\pi}^{-6\pi}\limits \sin \frac{x-3\pi}{6}\ \mathrm{d}x

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Spočtěte neurčitý integrál

\int 12x\left(x-7\right)^2dx.

3x^4-56x^3+294x^2+C

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2x^5-42x^4+294x^3-343x^2+C

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\frac{12}{5}x^5-\frac{7}{2}x^4+\frac{49}{3}x^3+C

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4x^4-84x^3+588x^2+C

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2x^5-42x^4+294x^3+C

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3x^4-294x^2+C

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Určete Taylorův polynom druhého stupně funkce

f(x)=\sin(5x+\pi)-2. se středem v bodě a=-\frac{\pi}{6}.

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

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

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

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

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

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Nalezněte obecné řešení rovnice

\sqrt{{1-y^2}}-y'x^{6}=0

y=\frac{\mathrm{sin} (x^{-5})}{-5}+C

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Žádná z předchozích odpovědí není správně.

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y=\mathrm{sin} (\frac{x^{7}}{7}+C)

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y=\mathrm{arcsin} (\frac{x^{-5}}{-5}+C)

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y=\mathrm{sin} (\frac{x^{-5}}{-5})+C

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Spočtěte neurčitý integrál

\displaystyle\int\frac{x-3}{\sqrt{x}}dx.

\displaystyle \frac{x+3}{2x\sqrt{x}}+C

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\displaystyle \frac{-6}{3}x^{\frac{3}{2}}+C

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\displaystyle \frac{x^2-6x}{2\sqrt{x}}+C

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\displaystyle \sqrt{\frac{x^2}{2}-6x+9\ln|x|}+C

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\displaystyle 2\sqrt{x}\left(\frac{x}{3}-3\right)+C

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\displaystyle \frac{x-6}{3\sqrt{x}}+C

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Určete Taylorův polynom druhého stupně funkce

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

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

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3+\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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3+\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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