Show that if $\lim_{x\rightarrow a}f'(x)=A$, then $f'(a)$ exists and equals $A$.
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
67364
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
64339
Find $f$ where $f'(x) = f(1+x)$
6620
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
83707
Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it.
60498
Prove that $\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$ does not exist
132824
Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
11879
If $\lim_{n\rightarrow\infty} f(n+1) - f(n) = L$, prove that $\lim_{n\rightarrow\infty} f(n)/n = L$
152132
Proving if $\lim_{n\rightarrow\infty}a_n=L $ then $\lim_{n\rightarrow\infty} \frac{a_1+a_2+\cdots+a_n}n=L $
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
121085
Showing that $\lim\limits_{x \rightarrow 0} \frac{1}{x}$ does not exist.
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous