If $f:R\to R$ is bounded on bounded intervals, and $\lim f(x+1) - f(x) = L$ for $x\to +\infty$ then $\lim f(x)/x = L$ when $x\to +\infty$
38831
If $\lim_{x\to+\infty}[f(x+1)-f(x)]= \ell,$ then $\lim\limits_{x\to+\infty}\frac{f(x)}x=\ell$.
94564
If $f$ is bounded and $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c}g(x)f(x) = 0$
36358
How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?
67292
Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$
142637
If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$
46156
How to find $\lim_{x \to \infty} [x]/x$?
142778
Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
117906
Show that $\liminf\limits_{x\to \infty}|f'(x)|=0$ if $\lim\limits_{x\to \infty}f(x)/x=0$ and $f$ is differentiable
119602
$f:\mathbb{R} \to \mathbb{R}$ be differentiable and $\lim\limits_{x\to\infty}f'(x)=1$, is $f(x)$ unbounded?
20764
Is it true that $\lim\limits_{x\to\infty}{x·P[X>x]}=0$?
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
76527
If $x_{m+n} \le x_n+x_m$, then $\lim x_n/n$ exists and is equal to $\inf x_n/n$
106060
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
11961
Why does $\lim_{n \to\infty}a_{n+1} = \lim_{n\to\infty}a_n$?
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
59162
Prove $\liminf\limits_{n\to\infty} F(x_n)\le F(x)$