lim(n→∞)An=x0=lim(n→∞)Bn，是否有 f'(x0)=lim(n→∞)[f(An)-f(Bn)]／(An-Bn) ？

moonlight1017

\(\displaystyle\lim_{n \to \infty}\alpha_n\)=\(x_0^+\),\(\displaystyle\lim_{n \to \infty}\beta_n\)=\(x_0^-\),\(f\)在\(x_0\)可导，那么\(\displaystyle\lim_{n \to \infty}{f(\alpha_n)-f(\beta_n)\over \alpha_n-\beta_n}\)是否等于\(f'(x_0)
\)?