If $f$ is continuous on $(0,1)$ and $\lim_{x \to 0^+}f(x) = +\infty$, show that $f$ is not uniformly continuous
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
10428
Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
106060
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
127868
If $f$ is nonnegative and integrable then $F(x) = \int_{-\infty}^x f$ is continuous.
117486
Limit of uniformly continuous functions with convergent improper integrals.
12997
Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
40297
Proof of uniform limit of Continuous Functions
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
135449
Prove: $\frac1x$ is not a uniformly continuous function
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$