how can I show that this function is uniformly continuous on $(1,0) $ and $(1,\infty)$
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
125024
Is this function uniformly continuous?
97256
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
36166
Uniform continuity on (0,1) implies boundedness
12349
a construction of a continuous function from a normal space to [0,1]
53627
Proving continuity of $f$
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
76607
Show that exists a continuous function in $E$ that is not bounded
126212
Proving uniform continuity on an interval
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
102918
Prove $\sin x$ is uniformly continuous on $\mathbb R$
134838
Uniform continuity of $f(x)=x^{2/3}\log x$ on $[0, \infty)$
60070
Unique uniformly continuous function into complete space
158567
A uniform continuous function which is not Hölder continuous
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists