设函数f(x)在点x0处可导,且f'(x0)=2,则lim(h→0)[f(x0-h/2)-f(x0)]/h等于多少
问题描述:
设函数f(x)在点x0处可导,且f'(x0)=2,则lim(h→0)[f(x0-h/2)-f(x0)]/h等于多少
答
lim(h→0) [f(x0 - h/2) - f(x0)]/h
= lim(h→0) [f(x0 - h/2) - f(x0)]/(- h/2) * (- 1/2)
= f'(x0) * (- 1/2)
= 2 * (- 1/2)
= - 1