$ \lim_{n\to \infty}\int_{0}^{1}\frac{2nx^{n-1}}{1+x}dx=?$
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
97747
Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
97571
Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{n}}$
68368
Evaluate $\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^{1/n} \ \mathrm{d}x$
18156
Find $\lim_{x\to \infty} \ln(x+1)/(\ln(x))$
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
102414
$\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to :
93408
Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
134787
How to prove $\lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1)$
76333
Let $b>0.$ Evaluate $\lim_{n \to \infty} \int^{b}_{0} \frac{\sin nx}{nx}dx$
117370
$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
101630
Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
101687
$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $
15982
Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$