Why $\lim_{x\to a} f(x) = f(a)$ in continuous function?
98271
Why does $(x \to a) ≠ (x = a)$ , But $f(x \to a) = f(x = a)$
100786
Does a continuous function take Cauchy sequences to Cauchy sequences?
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
131992
A problem on continuous functions
150554
proof that $f'$ is continuous at $a$
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
106060
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
138930
What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
25592
If a derivative of a continuous function has a limit, must it agree with that limit?
155333
Prove that $\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
53236
Formal proof of $\lim_{x\to a}f(x) = \lim_{h\to 0} f(a+h)$
50725
Inverse of function is continuous or not?
38659
Does any book now in print define the meaning of $\lim_{x\to a}f(x)=b$ for $f\colon E\to Y$, $E\subseteq X$, $X$ a topological space, $Y$ Hausdorff?
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
32571
Is the maximum function of a continuous function continuous?