Evaluate $\lim_{n \to \infty} \frac{1}{n}\int_{0}^{n}\frac{x\ln(1+\frac{x}{n})}{1+x}dx$
41515
fine the limit : $\lim_{ n \to \infty }\frac{1}{n}\int_{0}^{n}{ \frac{x\ln(1+\frac{x}{n})}{1+x}}=?$
148170
Difficulty in evaluating a limit: $\lim_{x \to \infty} \frac{e^x}{\left(1+\frac{1}{x}\right)^{x^2}}$
113913
using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
53109
Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
113289
finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
74204
Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
50243
Find $\lim_{n \to +\infty} \frac{1}{n}\sqrt[n]{\frac{(2n)!}{n!}} $ using Riemann integral
57573
Evaluate $ \lim_{n\to \infty} ( \lim_{x\to0} (1+\tan^2(x)+\tan^2(2x)+ \cdots + \tan^2(nx)))^{\frac{1}{n^3x^2}} $
20843
Evaluate the limit of $\lim_{n\to\infty}\frac{1}{n^2}\left(\frac{2}{1}+\frac{9}{2}+\frac{64}{9}+\cdots+\frac{(n+1)^{n}}{n^{n-1}}\right)$
41366
Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
125497
Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
147514
How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$?
115598
Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$
102414
$\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to :
130935
Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
76333
Let $b>0.$ Evaluate $\lim_{n \to \infty} \int^{b}_{0} \frac{\sin nx}{nx}dx$