What are different possible ways of proving that $\frac{\sin x}{x}$ is uniformly continuous?
113086
Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
5881
$\sqrt x$ is uniformly continuous
28730
product of two uniformly continuous functions is uniformly continuous
84785
Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
15284
$f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
24017
Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?
74258
Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
36741
Anti-derivative of continuous function $\frac{1}{2+\sin x}$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
154080
circular reasoning in proving $\frac{\sin x}x\to1,x\to0$
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
129073
If $f'$ is bounded, then $f$ is uniformly continuous
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$