proof check, ($ E(X^p)=\int_0^\infty px^{p-1}\mathbb{P}\{ X>x \}dx $)
5350
Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
52545
Prove limit converges in definition of $e.$
4287
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
88328
Proof of $1+x\leq e^x$ for all x?
35277
Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true?
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
34907
Show that $\int_{0}^{1}\{P(x)\}^{2}\,dx = (n + 1)^{2}\left(\int_{0}^{1}P(x)\,dx\right)^{2}$
125707
A simple proof (hopefully) for $2^x \neq 0$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
34496
Proof that $e=\sum\limits_{k=0}^{+\infty}\frac{1}{k!}$
64571
Prove that $\int_{E}f =\lim \int_{E}f_{n}$
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
26226
Proving $\lim \limits_{n\to +\infty } \left(1+\frac{x}{n}\right)^n=\text{e}^x$.