### Questions (77)

 5 Evaluate $\int\limits_{-\infty}^{\infty}\frac{\sin x}{x}\cdot\frac{\sin\frac{x}{3}}{\frac{x}{3}}\cdot\frac{\sin\frac{x}{5}}{\frac{x}{5}}dx$ 5 Find the sums of the series $S_1=\sum_{k=1}^\infty\frac{\cos^2 kx}{k^2}$ and $S_2=\sum_{k=1}^\infty\frac{\sin^2 kx}{k^2}$ 5 Prove that the series diverges 4 Prove the equality (Taylor series). 3 The easiest way to evaluate $I=\iint_D e^{-(x^2+y^2)}\,dx\,dy,\ \ \ D=\left\{(x,y)\Bigm|2\leqslant |x|+|y|\leqslant 3\right\}$

### Reputation (1,001)

 +10 Evaluate $I=\iint\limits_S yz^2\ dx\ dz\ \ \text{where}\ S\ \text{is the inner side of a cylinder}$ +10 Evaluate $I=\iint\limits_S (x^5+z)\ dy\ dz\ \ \text{where}\ S\ \text{is an inner side of a hemisphere}\ x^2+y^2+z^2=R^2,\ z\leqslant 0$ +10 Find the maximum and the minimum of the given function $u$ in the field $G$ +10 Prove that $\int\limits_{-\infty}^{+\infty}\frac{\sin x}{x}\cdot\frac{\sin(x/3)}{x/3}\dots\frac{\sin(x/15)}{x/15}\ dx<\pi$

 0 Find the Fourier series for $\sin^8x+\cos^8x$ 0 Find out whether the function is differentiable at the given point.

### Tags (49)

 0 calculus × 65 0 abstract-algebra × 8 0 sequences-and-series × 28 0 derivatives × 8 0 integration × 18 0 ordinary-differential-equations × 7 0 functions × 8 0 uniform-convergence × 7 0 multiple-integral × 8 0 ring-theory × 5

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