Prove that $\vert \tan^{-1}x-\tan^{-1}y \vert \le \vert x-y\vert\enspace \forall x,y \in ℝ$
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
118996
Prove that $T$ is an orthogonal projection
20467
Show that $(y_n)\in l^q$
94077
Proof of linear independence of $e^{at}$
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
6335
Proving that the set enclosed by an ellipse is convex
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
106609
Show that $e^{iy} = 1 + iy + \frac{\mu_1 y^2}{2}$ for all $y \in \mathbb{R}$ with $|\mu_1| \leq 1$
60761
Proof: $\cos^p (\theta) \le \cos(p\theta)$