Proving the function $f(x)=x^n$ is continuous
34940
Continuity of $f(x) = x^n$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
104044
Prove continuous functions $f$ and $g$ are equal
100740
proof of that a continuous function has a fixed point
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
2357
Showing $\frac{x^3y}{x^4+y^2}$ is continuous at all points
143174
property of continuous function
58664
Proving a function is continuous for a fixed variable
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
29276
technique of proving continuity complex function
38885
Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
125925
Convergence of $f_n(x)=x^n(1-x)^n$