Prove that the following limit exists $\lim_{n\to\infty}\left(\int\limits_{0}^{1}\vert f(x)\vert^{n}dx\right)^{\frac{1}{n}}$
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
148782
How to prove these two limits $\lim_{n\to\infty}\frac{a_{n}}{n}$ and $\lim_{n\to\infty}\frac{a_{n+1}-a_{n}}{n}$ exist?
63237
Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
128128
Show that $\lim_{n \to \infty} \left(1+\frac{a_n}{n}\right)^n= e^a$ when $a_n \to a$
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
44095
Prove that $\lim_{x\to \infty}\left(x-\ln\cosh x\right)=\ln 2$
91901
Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$
135731
Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
125497
Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
144403
Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
3619
Proof for $\lim_{n \to \infty}\left(1+\frac{a_n}{n}\right)^n = e^a$?
56265
limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
20089
Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$