Alfred Chern
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 17 Prove that a positive polynomial function can be written as the squares of two polynomial functions 8 sum of the series 7 Please prove: $\lim_{n\to \infty}\sqrt[n]{\frac{1}{n!}} = 0$ 6 Evaluate integral: $\int_0^{+\infty}\frac{\cos{bx}-\cos{ax}}{x}dx$ 6 An inequality on trace of product of two matrices

### Reputation (2,193)

 +5 Generalize Gauss-Bonnet Formula to non-simple closed curves +10 How find this limits $\lim_{n\to\infty}\left(\sin{\frac{\ln{2}}{2}}+\sin{\frac{\ln{3}}{3}}+\cdots+\sin{\frac{\ln{n}}{n}}\right)^{1/n}$ +10 How would you show that $\sqrt{14+4\sqrt{10}} - \sqrt{14-4\sqrt{10}} = 4$? +10 Evaluate integral: $\int_0^{+\infty}\frac{\cos{bx}-\cos{ax}}{x}dx$

### Questions (4)

 1 Generalize Gauss-Bonnet Formula to non-simple closed curves 1 Solution of parabolic PDE system 0 The functional $\int_0^{2\pi}\frac{\sqrt{1-\varphi^2-(\varphi')^2}}{1-\varphi^2}d\theta$ 0 Existence of the derivative

### Tags (62)

 32 real-analysis × 16 23 inequality × 10 31 calculus × 19 21 polynomials × 3 24 sequences-and-series × 13 14 linear-algebra × 10 24 analysis × 5 11 matrices × 6 23 limits × 13 10 algebra-precalculus × 12

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