Prove If $0<x<y$, then $x^{\frac{1}{n}}< y^{\frac{1}{n}},\, n\in \mathbb{N}$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
77973
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
66145
>Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
37489
Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
80440
Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
125707
A simple proof (hopefully) for $2^x \neq 0$
133190
Calculus - Prove $\lim_{n \to \infty} \frac{x^n}{n!}=0$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
149287
Prove that $A,B>0$ and $A_{ij}0$
20626
Prove that $x^y < y^x$