$\lim_{n\to\infty} \underbrace{\int_{0}^{1}\cdots \int_{0}^{1}}_{n}\frac{x_1^{505}+\cdots +x_n^{505}}{x_1^{2020}+\cdots +x_n^{2020}}dx_1\cdots dx_n$
53301
Problem with Infinite number of iterated integrals
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
65275
Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$
56902
Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$
47895
Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
144273
Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
4289
$\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
76990
Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$
147203
How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
13148
Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
36648
The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
50398
Limit $\lim\limits_{n\to\infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\frac{n}{n^2+3}+\cdots+\frac{n}{n^2+n}\right)$
109901
Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
83318
How to compute the limit $\lim_{n \to \infty} \sqrt[n]{a_1^n + \cdots + a_m^n}$?
80350
$\limsup \frac{a_n}{b_n}0$ s.t $a_n\le Mb_n$