$f:\mathbb{R} \to \mathbb{R}$ be differentiable and $\lim\limits_{x\to\infty}f'(x)=1$, is $f(x)$ unbounded?
68156
For a differentiable function $f:\mathbb{R} \rightarrow \mathbb{R}$ what does $\lim_{x\rightarrow +\infty} f'(x)=1$ imply? (TIFR GS $2014$)
49929
If $ \lim_{n \to \infty} (2 x_{n + 1} - x_{n}) = x $, then is it true that $ \lim_{n \to \infty} x_{n} = x $?
134787
How to prove $\lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1)$
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
155333
Prove that $\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$
20675
$L=\lim_{x\to\infty}(f(x)+f'(x))$ exists . Which of the following statements is\are correct?
36248
A classical problem about limit of continuous function at infinity and its connection with Baire Category Theorem
6417
Can a function be differentiable at the end points of its (closed interval) domain?
114702
$\int_0^{\infty} f(x)dx$ converges and $\lim_{x\rightarrow \infty} f(x)$ exists, then $\lim_{x\rightarrow \infty} f(x)=0$?
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
48464
If the derivative approaches zero then the limit exists
54321
Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative
84785
Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
157608
One-sided limits of $f'(x)$ at a point vs. one-sided limits of the difference quotient at that point
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
67364
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$