Prove that xf(x) is continuous with a specific case.
99795
Derivative of piece-wise function given by $x\sin\frac1x$ at $x=0$
151573
Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
52380
How to prove the function $e^x$ is continous for all real numbers
15914
Prove that any polynomial function is continuous
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
150770
Why is $f^n(\xi(x))$ continuous over $x$?
134752
Proof (epsilon delta) for the continuity of a function at a point
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
75479
Proving that this function is continuous on $G\times G$
23436
$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
105700
Proving $\,f$ is constant.