Show $|\frac{e^{-ixs}-1}{s}|\leq |x|$ , $x,s$ real.
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
103757
how can I prove that $\frac{\arctan x}{x }< 1$?
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
14951
Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$
6382
Showing $\frac{x}{1+x}0$ using the mean value theorem
123674
Show that $y = \frac{2x}{x^2 +1}$ lies between $-1$ and $1$ inclusive.
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
14677
Proving the exponential inequality: $x^y+y^x\gt1$
98768
Prove $\left(1+\frac{x}{n}\right)^n < e^x$, where $x$ is any positive real number and $n$ is any positive integer.
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
77130
How to prove this inequality $\left|x\sin{\frac{1}{x}}-y\sin{\frac{1}{y}}\right|<2\sqrt{|x-y|}$?
7775
Show that $|x-y|\leq |x|+|y|$.