Prove that $e^x>x+1 \forall x\ne 0$
58410
Simplest or nicest proof that $1+x \le e^x$
25775
How to prove $(1+1/x)^x$ is increasing when $x>0$?
101792
By expanding $e^x$ into a series prove the following inequality
154459
Constructing a HoTT proof term of 1≠0
52108
how to prove Exponential is strictly positive?
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
82775
if $a>1$, Prove that $\lim a^{1\over n}=1$
153123
Proving by induction $4^n  0$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
149739
Prove: $f(t)\leq t+1$
70129
Prove that in an ordered field $(1+x)^n \ge 1 + nx + \frac{n(n-1)}{2}x^2$ for $x \ge 0$
45555
$(x+y)^c\le x^c+y^c$ for $0<c\le1$