Let $f$ be a nonnegative continuous function on $[a,b]$, then $ \lim\limits_{n\to \infty} \left[\int^{b}_{a}f^{n}(x)dx\right]^{\frac{1}{n}}=M$
52711
Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
126256
Prove limit of function
3619
Proof for $\lim_{n \to \infty}\left(1+\frac{a_n}{n}\right)^n = e^a$?
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
144273
Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
41037
Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
28413
Limit of a continuous function
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
110208
limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$
9614
How does the existence of a limit imply that a function is uniformly continuous
68818
$\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$
113141
Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
102523
Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$
151568
Limit Integral equal to a supremun: $\lim_{n\to \infty} \left[\int_a^b (f(x))^n dx\right]^{{1}/{n}}=\sup_{x\in [a,b]} f(x).$