$f(x)=\frac{\sin x}{x}$, prove that $|f^{(n)}(x)|\le \frac{1}{n+1}$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
123490
L'Hopital's rule and $\frac{\sin x}x$
63523
$|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. Prove $(a_n)$ is Cauchy
48824
Prove: $ \frac{1}{\sin 2x} + \frac{1}{\sin 4x } + \cdots + \frac{1 }{\sin 2^n x} = \cot x - \cot 2^n x $
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
137844
Proof of $\sin nx=2^{n-1}\prod_{k=0}^{n-1} \sin\left( x + \frac{k\pi}{n} \right)$
18285
Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$
84681
Multiple choice exercise on $f(x)= \frac {\sin x}{|x|+ \cos x}$
50972
Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
145909
Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
2414
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$
63553
Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$
91000
Prove that $\frac{1}{a+1}0$
16418
Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing