Prove that $ \lim_{n \to \infty}\int_0^{n^2} n\sin (x/n)e^{-x^2} dx = 1/2 $
39798
Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
81090
Calculate $\lim_{n\to\infty}(\sqrt{n^2+n}-n)$.
122301
Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
29287
Prove that: $\lim_{n\to\infty} f(n+1) - f(n) = \lim_{x\to\infty} (f(x))' $
64571
Prove that $\int_{E}f =\lim \int_{E}f_{n}$
49489
Compute $\lim_{n\to\infty} \int_{0}^{\pi/4}\tan^n x \ dx$
122820
Prove $\lim_{n\to\infty}x_n=2$ Given $\lim_{n \to \infty} x_n^{x_n} = 4$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
106527
Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
68368
Evaluate $\lim_{n \to \infty} \int_{0}^1 [x^n + (1-x)^n ]^{1/n} \ \mathrm{d}x$
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
140574
Find $\lim_{n\to \infty} \int_0^1 nx^n e^{x^2} dx$
4345
Prove that lim $(\sqrt{n^2+n}-n) = \frac{1}{2}$
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
50673
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
144310
How would you prove that $\lim\limits_{n\to\infty}(\sqrt{4n^2+n}-2n)=\frac14$?