Prove that $e^{x} \geq x^{e}$ for all $x \geq 0$.
53583
Why $e^x$ is always greater than $x^e$?
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
6450
Show $\mathbb{E}[f(X)g(X)] \geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$ for $f,g$ bounded, nondecreasing
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
107058
Prove that $E(X\ln X)\le E X E\ln X$
90796
Inequality Regarding e
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
146180
Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
21923
Prove that $\exp(x)>0$ using only formal definition of exp
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
39270
Showing that $e^x > 1+x$
39943
Proving $\mathrm e <3$
16798
Prove the inequality $n! \geq 2^n$ by induction
88838
How can I prove this inequality for $n\geq 2$?
23946
Prove the definitions of $e$ to be equivalent
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$