Prove that $f(x)=x\sin(x)$ is not a uniformly continuous function
3856
Uniform Continuity of $x \sin x$
63418
Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$
16642
Showing $a_n=\sin(n)$ does not converge
117419
Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
83915
Showing that a function is not differentiable
113740
Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
99726
Proving that a function is not a contraction
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
75137
proving that $f(x) = x^s$ is holder continuous with holder exponent s
102918
Prove $\sin x$ is uniformly continuous on $\mathbb R$
35953
Prove that a function is not injective
65346
Characterisation of uniformly continuous function
150554
proof that $f'$ is continuous at $a$
55368
$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly