Is $x\sin\left(\frac{1}{x}\right)$ uniformly continuous in $\mathbb{R}$?
26373
Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
26291
Does $\frac{nx}{1+n \sin(x)}$ converge uniformly on $[a,\pi/2]$ for all $a \in (0,\pi/2]$?
40297
Proof of uniform limit of Continuous Functions
157308
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be continuous.Let $t\in\mathbb{R}$. Evaluate:$\lim_{h\rightarrow0}\frac{1}{h}\int_{t-h}^{t+h}f(s)ds$
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
96112
Differentiating $ \left( 1 - \frac {1}{x} \right)^x $
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
46642
Continuity of $\sin(x)/x$
122073
Computing $\lim_{n \rightarrow\infty} \int_{a}^{b}\left ( f(x)\left | \sin(nx) \right | \right )$ with $f$ continuous on $[a,b]$
88640
Is $\sqrt x$ continuous at $0$? Because it is not defined to the left of $0$
25010
Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
65346
Characterisation of uniformly continuous function
142928
Proving $\left\{ \frac{1}{n} \right\}$ is Cauchy
19167
Show that $X_{n}\sim N(\sin(\pi n),1)$ is uniformly tight
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous