What can we say about $\alpha$ if $\lim_{x\to \infty}f(x)=1$ and $\lim_{x\to \infty}f'(x)=\alpha$ for a differentiable function $f$ on $\mathbb{R}$?
10428
Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
140884
Limits and derivatives - two questions
151109
Verification that $\lim_{x \to a}\frac{f(x)-f(a)}{x-a}$ and $\lim_{h\to 0}\frac{f(a+h) -f(a)}{h}$ are equivalent definitions of the derivative.
49781
Existence of the absolute value of the limit implies that either $f \ $ or $\bar{f} \ $ is complex-differentiable
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
20956
Correct way to prove the limit: $\mathop {\lim }\limits_{x \to 0} {x^\alpha }\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^{\alpha  + 1}}}}dt} $?
120118
The distinction between infinitely differentiable function and real analytic function
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
119200
When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail
41037
Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
35435
For what values of $\alpha$, does this integral converge?
13104
What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
69808
For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge?
36060
If $\lim_{n\to\infty}x_n=\alpha$, show $\lim_{n\to\infty}(x_1x_2\dots x_n)^{1/n} =\alpha$.
36358
How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?