If $\displaystyle \lim _{x\to +\infty}y(x)\in \mathbb R$, then $\lim _{x\to +\infty}y'(x)=0$
5371
If a function has a finite limit at infinity, does that imply its derivative goes to zero?
67364
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
17019
Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$
17069
Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
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
79182
what is the limit of $\displaystyle \lim_{x\to 0} \frac{x}{a}\cdot \lfloor{\frac{b}{x}\rfloor}$
44551
What is the result of $ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $ and why?
114675
Evaluating $\lim\limits_{x\to 0}(1+x)^{1/x}$?
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 $a, b \in \mathbb{R}$
138930
What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
49511
Do we have $\lim_{h\to 0^+}\int_0^\infty|f(t+h)-f(t)|dt=0$?
64485
Proving $\displaystyle\lim_{h\to0}\frac{f(x+h)-2f(x)+f(x-h)}{h^2}=f''(x)$
36358
How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?
104229
Show that $\lim\limits_{y\downarrow 0} y\mathbb{E}[\frac{1}{X};X>y]=0$.
116423
What is wrong with the argument $1 = \lim_{n\to \infty} n/n = \lim_{n\to\infty} (1/n+1/n+\dotsb+1/n) = 0 $?
37251
Values of the limit $\lim\limits_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$