7 Integrate without expansion? 5 Proving an Intuitive Result Rigorously 5 Prove that second partial derivatives are not equal 4 Calculation of a series using series definition 4 Prove that a function is indefinitely differentiable

### Reputation (1,109)

 +10 Prove that second partial derivatives are not equal +45 Determine whether the improper integral $\int_{1}^{\infty} \frac{1}{x^3\sqrt{x^2 -1}} dx$ converges +10 Hint for integral of a function +10 Is it always true that the integral of cos and sin to an odd power from $0$ to $2\pi$ is always $0$?

### Questions (7)

 4 How to prove $\lim_{n \rightarrow \infty } \frac{1}{n} \int_0^1 \ln \big( 1 + e^{nf(t)} \big) dt = \int_0^1 f^+(t) dt$ 3 Convergence of sequence of function 2 Connecting integral involve integer and half-integer Bessel function 1 Uniformly convergence and Uniformly continous 1 Proving Liouville's theorem on $R^n$

### Tags (36)

 40 calculus × 22 9 real-analysis × 13 15 integration × 8 9 functions × 3 15 limits × 8 7 analysis × 6 15 sequences-and-series × 6 5 convergence × 3 10 derivatives × 3 5 partial-derivative

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