Limit $\lim_{n \to \infty} \int_{0}^{1} n x^n f(x) dx $
5229
Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
76333
Let $b>0.$ Evaluate $\lim_{n \to \infty} \int^{b}_{0} \frac{\sin nx}{nx}dx$
59162
Prove $\liminf\limits_{n\to\infty} F(x_n)\le F(x)$
51212
How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
155513
I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $
41515
fine the limit : $\lim_{ n \to \infty }\frac{1}{n}\int_{0}^{n}{ \frac{x\ln(1+\frac{x}{n})}{1+x}}=?$
6990
For $f$ Riemann integrable prove $\lim_{n\to\infty} \int_0^1x^nf(x)dx=0.$
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
50682
Prove: $\lim\limits_{n \to \infty} \int_{0}^{\sqrt n}(1-\frac{x^2}{n})^ndx=\int_{0}^{\infty} e^{-x^2}dx$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
4289
$\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
112285
Show that $\lim_{x\to\infty} f(x)=0 \implies \lim_{x\to\infty} f'(x)=0$
18079
Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
20764
Is it true that $\lim\limits_{x\to\infty}{x·P[X>x]}=0$?
65137
Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$