Bonrey

### Questions (71)

 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 (957)

 -2 How to evaluate $\text{Li}_2(z)+\text{Li}_2\left(\frac{1}{z}\right)$? +10 Prove that $\int\limits_{-\infty}^{+\infty}\frac{\sin x}{x}\cdot\frac{\sin(x/3)}{x/3}\dots\frac{\sin(x/15)}{x/15}\ dx<\pi$ +10 Evaluate $I_1=\int_{-\infty}^{+\infty}\frac{\cos 3x}{5+6x+9x^2}dx$ using Fourier transform. +10 The easiest way to evaluate $I=\iint_D e^{-(x^2+y^2)}\,dx\,dy,\ \ \ D=\left\{(x,y)\Bigm|2\leqslant |x|+|y|\leqslant 3\right\}$

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

### Tags (42)

 0 calculus × 61 0 multiple-integral × 8 0 sequences-and-series × 29 0 derivatives × 8 0 integration × 13 0 functions × 7 0 ordinary-differential-equations × 8 0 uniform-convergence × 7 0 abstract-algebra × 8 0 ring-theory × 5

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