24 How to solve this equation manually: $(x^2+100)^2=(x^3-100)^3$? 12 Proof of value of infinite series, using definition of the integral 11 Prove that $f'(1)=0$ if $f(x^2)-\sin f(x)=1$ 9 Solving for the CDF of the Geometric Probability Distribution 7 Writing $1/(X+i\epsilon)$ in terms of principal value and imaginary part

### Reputation (6,061)

 +10 Find the marginal distribution of $V=X-Y$ +20 Simplest proof that a rank-1 matrix with prescribed row and column sums is unique +10 Writing $1/(X+i\epsilon)$ in terms of principal value and imaginary part +10 How to take the derivative of product of a sequence?

### Questions (30)

 17 Find the simplest counterexample against exchanging limit and summation 5 Probability of winning/losing a lonely card game when you shout an integer progressively each time you draw 5 Nasty logarithmic infinite sums arising from a tan integral 5 Asymptotic of an integral involving sine and erf 4 Expansion of Gaussian function in a series of exponential functions

### Tags (130)

 107 calculus × 57 44 probability × 39 89 limits × 37 40 sequences-and-series × 17 85 integration × 55 28 algebra-precalculus × 5 66 real-analysis × 24 22 probability-distributions × 18 56 definite-integrals × 39 22 summation × 6

### Bookmarks (20)

 12 Closed form for $\int_0^1...\int_0^1\frac{1}{\left(1+\sqrt{1+x_1^2+...+x_n^2}\right)^{n+1}}\;dx_1...dx_n$ 11 (Non)Existence of limits 6 Solve $\int_0^1 \int_0^{2\pi}\frac{ax-x^2\sin(\theta)}{\sqrt{a^2-2ax\sin(\theta)+x^2}}d\theta dx$ 4 Limit with the Appell F1 function 4 Are real antisymmetric matrices orthogonally similar to their transposes?