limit of integral of $~f(x+t)-f(x)~$.
37055
Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$
88226
Limit of a stochastic integral
10093
$\lim_{x\to \infty}e^{-x^2}\int_x^{x+1/x}e^{t^2}dt$
64571
Prove that $\int_{E}f =\lim \int_{E}f_{n}$
105569
If $f$ is integrable in $[a-1,b+1]$, then prove that $\lim \limits_{h\to 0} \ \int_{a}^{b}|f(x+h)-f(x)| ~ dx=0$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
86409
Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
60792
Limit of divided integrals
79368
Can a limit of an integral be moved inside the integral?
5402
Prove or the disprove the existence of a limit of integrals
10408
Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
36648
The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
138169
Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
50472
If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$
2239
Showing that $\{f_n \}$ converges to $f$ is equivalent to $\lim_{n\to \infty} \int_X \frac{|f_n(x)-f(x)|}{1+|f_n(x)-f(x)|}d\mu(x)=0$