Why is it true that $\lim_{n\to\infty} \left(\int_a^b \left|f(x)\right|^ndx\right)^{1/n} = \text{sup}\{\left|f(x)\right| : x \in [a,b]\}$?
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
50673
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
36060
If $\lim_{n\to\infty}x_n=\alpha$, show $\lim_{n\to\infty}(x_1x_2\dots x_n)^{1/n} =\alpha$.
43703
Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
23217
About $\lim \left(1+\frac {x}{n}\right)^n$
135155
Why is $\lim_{n \to +\infty }{\sqrt[n]{a_1 a_2 \cdots a_n}} =\lim_{n \to +\infty}{a_n}$
101027
What is the value of lim$_{n\to \infty} a_n$ if $\lim_{n \to \infty}\left|a_n+ 3\left(\frac{n-2}{n}\right)^n \right|^{\frac{1}{n}}=\frac{3}{5}$?
22575
Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$
25206
How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
138930
What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
20764
Is it true that $\lim\limits_{x\to\infty}{x·P[X>x]}=0$?
122769
Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
141852
Prove that $2\int_a^b \int_a^x f(x)f(y) \, dy \, dx = \left[ \int_a^b f(x) \, dx \right]^2$
73934
Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$
17329
How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?