设函数f(x)在x=a处的导数为f'(a),求limh→0 f^2(a)-f^2(a-h)/h 答案为2f(a)f'(a)

问题描述:

设函数f(x)在x=a处的导数为f'(a),求limh→0 f^2(a)-f^2(a-h)/h 答案为2f(a)f'(a)

limh→0 f^2(a)-f^2(a-h)/h
=limh→0 [f(a)+f(a-h)][f(a)-f(a-h)]/h
=2f(a)f'(a)请问[f(a)+f(a-h)] 怎么就等于2f(a)了呢?limh→0[f(a)+f(a-h)] =2f(a)