Proving $x^n$ is continuous for all $n$
103932
How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?
150770
Why is $f^n(\xi(x))$ continuous over $x$?
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
5881
$\sqrt x$ is uniformly continuous
104602
asymptotic of $x^{x^x} = n$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
108429
Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
72044
prove $x \mapsto x^2$ is continuous
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
158569
Proving a particular subset of $R^n$ is closed
1986
Show $1/(1+ x^2)$ is uniformly continuous on $\Bbb R$.
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
31548
Proof of "every convex function is continuous"
38885
Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
147841
Please help prove that $(x_n)$ is a Cauchy sequence if $|x_{n+1} - x_n| \leq Cr^n$
87239
Prove functions defined by sup and inf are continuous
13257
How to prove this problem about uniform continuity