Prove inequality $e^{x}>1+x$
39270
Showing that $e^x > 1+x$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
77026
Proof with inequalities
129584
How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
117262
Proving a logarithm inequality
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
80556
Demonstrate by induction the inequality: $\ln(1+n)\leq\sum_{i=1}^{n}\frac{1}{i}\leq1+\ln(n)$
98768
Prove $\left(1+\frac{x}{n}\right)^n < e^x$, where $x$ is any positive real number and $n$ is any positive integer.
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
90896
proof of inequality $e^x\le x+e^{x^2}$
20626
Prove that $x^y < y^x$
15237
Prove an inequality using complex analysis
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
101792
By expanding $e^x$ into a series prove the following inequality
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
8207
Can I prove this inequality algebraically?