Evaluating $\lim_{n \to \infty} \int_{0}^{1} n(2^x-1)^n dx$
97256
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
44054
Evaluating the integral $\mathop{\lim}\limits_{n \to \infty} \int_{-1}^{1} f(t)\cos^{2}(nt) \ dt $
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
138169
Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
110208
limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$
114481
Calculating $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$
74204
Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
124699
How to calculate $\lim_{n \to \infty}\sqrt[n]{\frac{2^n+3^n}{3^n+4^n}}$
81997
Evaluating $\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$
101630
Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$
131023
Evaluate the sum: $\sum\limits_{n=0}^{\infty} \frac1{F_{(2^n)}}$
24941
How to evaluate $\lim_{n\to\infty}n!/n^{k}$
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
5974
Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
133244
Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$