Proof of the inequality $e^x\le e^{x^2} + x$
90896
proof of inequality $e^x\le x+e^{x^2}$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
91617
Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
117262
Proving a logarithm inequality
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
126557
Proving the inequality $\sum_{\text{cyc}} \frac{a}{a^2+b^3+c^3}\le\frac1{5abc}$
97253
How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$
110368
Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
29342
Prove the inequality: $(y+z)*x^4+(x+z)*y^4+(x+y)*z^4\le((x+y+z)^5)/12$ for positive reals.
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
142922
How to prove that $e^x$ is convex?
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
101499
Prove $e^{x+y}=e^{x}e^{y}$ by using Exponential Series