• January 5th 2012, 03:36 AM
mami
$\lim_{n\to\infty}\int_{0}^{\sqrt{n}}\left(1-\frac{\left x^2\right}{n}\right )^{n}dx$
It can be useful the substitution $t=x/\sqrt{n}$, so $\int_{0}^{\sqrt{n}}(1-x^2/n)^n\;dx=\sqrt{n}\int_{0}^{1}(1-t^2)^n\;dt$ .