Show that for $\eta > 0$, $\alpha_\eta=-\infty$
101166
Show that for $\eta > 0$, $\alpha_\eta=-\infty$ and for the Cauchy problem $z'=x-z^2,z(0)=\eta$ the saturated solution is defined up to $+\infty$.
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
95862
Prove that $t_{n-1, \alpha/2}$ is strictly decreasing in $n$
135941
Derivative of $|x|^\alpha$
48686
Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$
136195
Stuck trying to prove that $e^{-x^{-2}}$ is $C^{\infty}$
110275
Let $p>0$. Show the $\lim_{n\to\infty}(a^n/n^p)$ is equal to:
44737
$ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
142168
can we a prove ⊢ (α → α) → (α → α)
122769
Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
100642
Proof of the L'Hôpital Rule for $\frac{\infty}{\infty}$
136421
How to prove convergence of $\sum\limits_{n=1}^\infty \frac{\sqrt a_n}{n^\alpha}$
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
12301
Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$