If $f$ is differentiable at $a$, then $\lim_{x\rightarrow a}f(x)$ exists.
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
128218
If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
6417
Can a function be differentiable at the end points of its (closed interval) domain?
43874
Differentiability implies continuity - A question about the proof
71738
Continuously differentiable function iff $|f(x + h) - f(x + t) - l(h - t)| \leq \epsilon |h-t|$
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
12498
Derivable function on an interval $ [a,b]$ with derivative unbounded on $[a,b]$
15579
Show that $f$ is uniformly continuous if limit exists
33130
$f$ differentiable except in $1$ point
154881
Question on differentiability of a continuous function
150005
Existence of points in a differentiable function
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
26424
If $f(x)<g(x)$ prove that $\lim f(x)<\lim g(x)$
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?