LeL $f: (0, \infty)\to R$ be continuous and $f(x)\leq f(nx)$ prove $\lim\limits_{x\to\infty} f(x)$ exists
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
11879
If $\lim_{n\rightarrow\infty} f(n+1) - f(n) = L$, prove that $\lim_{n\rightarrow\infty} f(n)/n = L$
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
121217
How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?
155333
Prove that $\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
50682
Prove: $\lim\limits_{n \to \infty} \int_{0}^{\sqrt n}(1-\frac{x^2}{n})^ndx=\int_{0}^{\infty} e^{-x^2}dx$
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
13561
Show: $E(|X|)\leqslant\liminf_{n\to\infty} E(|X_n|)$
74170
Prove that $\lim_{x \to +\infty} \frac{f(x)}{x} = L$ if $\lim_{x \to +\infty} [f(x+1) - f(x)] = L \space$
50472
If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$
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
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$