Prove: $\lim_{h\to0}\int_{-\infty}^{+\infty}|f(x+h)-f(x)|^p\mathrm dx=0$
37055
Show that $\lim _{r \to 0} \|T_rf−f\|_{L_p} =0.$
153267
Proving $\lim\limits_{x \to \infty} xf(x)=0$ if $\int_{0}^{\infty}f(x) dx$ converges.
112285
Show that $\lim_{x\to\infty} f(x)=0 \implies \lim_{x\to\infty} f'(x)=0$
8829
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$
109907
How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
132738
Showing $\lim_{n \to \infty} m(E_n) = 0$, assuming $f > 0$ a.e. and $\lim_{n \to \infty} \int_{E_n}f \,dm =0$
42817
proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
103513
Show that $\lim_{n\to \infty}\int_{-\pi}^{\pi}f(x)g(nx)\,dx=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)\,dx\int_{-\pi}^{\pi}g(x)\,dx$
19986
How can this be proved $\lim_{x\to\infty}(f(x)+f'(x))=l$
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
105569
If $f$ is integrable in $[a-1,b+1]$, then prove that $\lim \limits_{h\to 0} \ \int_{a}^{b}|f(x+h)-f(x)| ~ dx=0$
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
88792
Convergence of $\int_0^\infty $sin$ (x^p) dx$
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
122769
Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$