how to prove that $\exp(x)\geq x+1$
58410
Simplest or nicest proof that $1+x \le e^x$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
39270
Showing that $e^x > 1+x$
52380
How to prove the function $e^x$ is continous for all real numbers
40420
Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
156669
Trying to prove a simple (?) inequality
95684
Show that $g'(x)+g(x)-2e^x=0$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
19078
Prove an interpolation inequality
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
12781
Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
91000
Prove that $\frac{1}{a+1}0$