设函数f(x)在点x0处可导,求lim(h→0)(f(x0+h)-f(x0-h))/2h的值

=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)