Proving uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ on $(1,2)$ directly from the definition.
26373
Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
135449
Prove: $\frac1x$ is not a uniformly continuous function
1986
Show $1/(1+ x^2)$ is uniformly continuous on $\Bbb R$.
29276
technique of proving continuity complex function
134752
Proof (epsilon delta) for the continuity of a function at a point
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
158567
A uniform continuous function which is not Hölder continuous
36166
Uniform continuity on (0,1) implies boundedness
97553
Continuity of $\frac{2xy}{x^2+y^2}$ at $(0,0)$
3856
Uniform Continuity of $x \sin x$
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$
105700
Proving $\,f$ is constant.
15284
$f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
58664
Proving a function is continuous for a fixed variable
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.