设函数f(x)在点x0处可导,求lim(h→0)(f(x0+h)-f(x0-h))/2h的值
问题描述：
设函数f(x)在点x0处可导,求lim(h→0)(f(x0+h)-f(x0-h))/2h的值
答
令a=x0-h
则原式=lim(h→0)(f(a+2h)-f(a))/2h
=f'(a)
=lim(h→0)f'(x0-h)
=f'(x0)
答
=lim(h→0)(f(x0+h) - f(x0) + f(x0) -f(x0-h))/2h
=(1/2)lim(h→0)(f(x0+h) - f(x0) )/h + (1/2)lim(h→0)(f(x0-h) - f(x0) )/(-h)
=(1/2)f'(x0) + (1/2)f'(x0)
= f'(x0)