Proving $\lim_{h \to 0} \frac{|h|^\alpha}{h}=0$ given $\alpha > 1$.
135941
Derivative of $|x|^\alpha$
36060
If $\lim_{n\to\infty}x_n=\alpha$, show $\lim_{n\to\infty}(x_1x_2\dots x_n)^{1/n} =\alpha$.
91000
Prove that $\frac{1}{a+1}0$
117246
Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
103055
Proving the quotient rule for limits
145632
Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
146827
show that $\limsup(\frac{n!}{n^n})=0$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
1444
Prove/Show that Limit is equal to 0.
13696
Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$
95991
How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?
12865
Prove that $\lim_{n\to\infty} H_n/n = 0$ ($H_n$ is the $n$-th harmonic number) using certain techniques
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
67894
$\epsilon$-$\delta$ proof that $\lim\limits_{x \to 1} \frac{1}{x} = 1$.
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$