Prove that $e^x-x\geq 1$.
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
29679
Prove: $|x-y|\leq |x|+|y|$
119668
How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|$?
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
95684
Show that $g'(x)+g(x)-2e^x=0$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
3820
Prove that $||x|-|y||\le |x-y|$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
101792
By expanding $e^x$ into a series prove the following inequality
107058
Prove that $E(X\ln X)\le E X E\ln X$
88838
How can I prove this inequality for $n\geq 2$?
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
126032
Proving a certain inequality
8207
Can I prove this inequality algebraically?