Proof that $x^y + y^x > 1 \ \forall x,y > 0 $
33332
A classic exponential inequality: $x^y+y^x>1$
90896
proof of inequality $e^x\le x+e^{x^2}$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
32407
Prove $\exp(x+y) = \exp(x) \exp(y)$ for $\exp(x) = \sum_{n=0}^\infty \frac {x^n}{n!}$
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
144713
Simple Calculus Proof
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
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$
106934
$x^x=y$. How to solve for $x$?
96153
$ x^3<y^3 \iff x<y $ proof issue.