Determine if $h(x)=\sin(x^2)$ is uniformly continuous on $(-\infty,\infty)$
37812
Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
40297
Proof of uniform limit of Continuous Functions
155170
Proving $\sin(x^2)$ Continuous but Not Uniformly Continuous with non-standard Definition
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
15579
Show that $f$ is uniformly continuous if limit exists
125745
continuity of power series
156736
Prove that $\lim _{x \to \infty} x\sin x$ doesn't exist (using delta epsilon).
102918
Prove $\sin x$ is uniformly continuous on $\mathbb R$
131485
Continuity of $\frac{x^3y^2}{x^4+y^4}$ at $(0,0)$?
149601
$\lim_{x\to{\infty}} (x-\sqrt{x^2+x})$
86860
Continuity of differentiable function $x^2\sin(1/x)$
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
112951
Improper integral $\sin(x)/x $ converges absolutely, conditionaly or diverges?
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
12997
Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?