Why is $\lim_{n \to \infty} \int_{0}^{1} { {nx^{n-1}} \over {1+x} }dx=1/2$?
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
138930
What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
89421
Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
58456
Why is $ 1^{\infty} \not= \lim_{t \to \infty} 1^t = 1$?
81654
Evaluate $\lim_{n\to\infty} [{1\over kn}+{1\over k(n+1)}+{1\over k(n+2)}+\cdots+{1\over k(n+p-k)}]$ where $k<p$
126374
Limit of $2^{1/n}$ as $n\to\infty$ is 1
49074
Compute $\int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx$ via residue calculus.
18156
Find $\lim_{x\to \infty} \ln(x+1)/(\ln(x))$
111636
Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$
17329
How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?
46156
How to find $\lim_{x \to \infty} [x]/x$?
86843
Find the value of : $\lim_{n\to\infty}[(n+1)\int_{0}^{1}x^{n}\ln(1+x)dx]$.
149601
$\lim_{x\to{\infty}} (x-\sqrt{x^2+x})$
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
106087
Finding $\lim_{n \to \infty} \int_1^a \frac{n}{1+x^n} \, dx$
107351
Evaluate the improper integral $\int_{0}^{\infty}{f(x)-f(2x)\over x}dx$, where $\lim_{x \to \infty} f(x) = L$
37277
$\lim\limits_{n \to{+}\infty}{\sqrt[n]{n!}}$ is infinite