How to prove: $e^x \ge x^e$ for $x>0$
53583
Why $e^x$ is always greater than $x^e$?
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
138962
$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
111406
Proving that a definition of e is unique
33332
A classic exponential inequality: $x^y+y^x>1$
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
83386
Inequality with exponents $x^x+y^y \ge x^y +y^x$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
118467
Prove that $a^2+ab+b^2\ge 0$
95415
proof relating to limit definition of e
117262
Proving a logarithm inequality
109295
Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
52545
Prove limit converges in definition of $e.$
108704
Help with proof of $|x+y| \geq |x|-|y|$