Proving $L_{p}$ Norm When $p\to \infty (or \|x\|_{\infty})$
10383
The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
45988
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
154913
Are all the norms of $L^p$ space equivalent?
48792
Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$
144382
Proving $\lVert x \rVert_3$ is smaller than euclidean norm
3273
Trouble in proving that $\|x\|_p = \max|x_j|$
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
91750
$l^p$ not norm, $p<1$
154247
Proving $f(x)$ attains $\max$ or $\min$ when $f(x)\to0$ as $|x|\to\infty$.
13732
$||f||_p\to ||f||_\infty$ under general assumptions
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
139595
Show that $(l_1)^* \cong l_{\infty}$
31672
$L^p$-norm of the gradient of a harmonic function.
91901
Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$