Find the value of $\lim_{n\to\infty} \int_0^1 \frac{nx^{n-1}}{x+1}dx$
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
128181
Find $\lim_{n\to\infty}{\sqrt{n+1}-\sqrt{n}}$ with basic methods
17534
Find $\lim_{n\to \infty}({1\over \sqrt{n^2+1}}+{1\over \sqrt{n^2+2}}+\cdots+{1\over \sqrt{n^2+n}})$
25193
Find $ \lim _{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n}$
49860
Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$
101630
Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
57686
Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
54775
Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
49489
Compute $\lim_{n\to\infty} \int_{0}^{\pi/4}\tan^n x \ dx$
60831
Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
109899
Find $\,\lim_{x\to 1}\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}$
107237
Evaluate $\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$
112621
Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
152557
Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
109059
Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$