$f(x)=x\cdot \ln(x)$ uniformly continuous in $(0, \infty)$
127538
Show $f(x)=x\ln x$ is not uniformly continuous
134838
Uniform continuity of $f(x)=x^{2/3}\log x$ on $[0, \infty)$
74145
How to prove $x^{n}$ is not uniformly continuous
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
110146
I need to prove the continuity of $f(x)=\log x$ using a $\epsilon-\delta$ proof
5881
$\sqrt x$ is uniformly continuous
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
113086
Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
28730
product of two uniformly continuous functions is uniformly continuous
124463
Integral from $0$ to $\infty$ of $\ln(x)/e^x$
126212
Proving uniform continuity on an interval
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$
130161
Showing that if $\lim_{x\to\infty}xf(x)=l,$ then $\lim_{x\to\infty}f(x)=0.$
124779
Intuition for uniform continuity of a function on $\mathbb{R}$