The proof of $e^x \leq x + e^{x^2}$
90896
proof of inequality $e^x\le x+e^{x^2}$
104498
Show that $x^3y^3(x^3+y^3) \leq 2$
14677
Proving the exponential inequality: $x^y+y^x\gt1$
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
146180
Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
106609
Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
20964
Proof that $n^2 < 2^n$
40420
Proof by induction of Bernoulli's inequality: $(1 + x)^n \geq 1 + nx$
125707
A simple proof (hopefully) for $2^x \neq 0$
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
40549
How to proof the the derivative of $x^2$ is $2x$?
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
58410
Simplest or nicest proof that $1+x \le e^x$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$