计算$\lim_{n\to \infty}\int_{0}^{1}e^{-n x^2}dx$
解答：由Taloy公式知
$$e^{-nx^2}=\frac{1}{1+n x^2+...} \leq \frac{1}{1+n x^2}$$
而易求得
$$\lim_{n\to \infty}\int_{0}^{1}\frac{1}{1+nx^2}dx=0$$
