Prove the limit of the integral
39798
Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
151568
Limit Integral equal to a supremun: $\lim_{n\to \infty} \left[\int_a^b (f(x))^n dx\right]^{{1}/{n}}=\sup_{x\in [a,b]} f(x).$
129042
Prove that $\lim_{a \to 0^{+}} \int_{0}^{a} \frac{1}{\sqrt{\cos(x)-\cos(a)}} \;dx=\frac{\pi}{\sqrt{2}}$
128189
Proving Integral Inequality
126256
Prove limit of function
155333
Prove that $\lim_{x\to\infty}\frac{f(x)}x=\lim_{x\to\infty}f'(x)$
1234
Evaluating limits of integrals
103374
A Problem on Improper Integrals
20089
Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$
152640
show that $\lim(\pi(x)/x) = 0$
6878
Prove limit of sequence
78444
Limit of definite integral of $f(x)\cos(mx)$
5430
Using Cauchy's integral theorem to prove a inequality
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
44095
Prove that $\lim_{x\to \infty}\left(x-\ln\cosh x\right)=\ln 2$