If $\lim_{x\to0}f'(x)=l$, then is it true that $f'(0)=l$.
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
107795
If $\,f''(x) \ge f(x)$, for all $x\in[0,\infty),$ and $\,f(0)=f'(0)=1$, then is $\,f(x)>0$?
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
21954
A question about $f(x)\equiv 0$
99906
If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
11879
If $\lim_{n\rightarrow\infty} f(n+1) - f(n) = L$, prove that $\lim_{n\rightarrow\infty} f(n)/n = L$
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
34187
The limit of the derivative of an increasing and bounded function is always $0$?
149586
If $\lim_{x\to\infty} f'(x) = L$, prove that $\lim_{x\to\infty} f(x+c)-f(x) = cL$ and $\lim_{x\to\infty} f(x)/x=L$
38831
If $\lim_{x\to+\infty}[f(x+1)-f(x)]= \ell,$ then $\lim\limits_{x\to+\infty}\frac{f(x)}x=\ell$.
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
36358
How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?
39747
Showing that $\lim_{x\to 0} x\log{x}= 0$ without using L'Hopital's rule
49511
Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?