已知f(a)的导数=3 则lim(h趋向于0) f(a+3h)-f(a-h) /h=?

问题描述:

已知f(a)的导数=3 则lim(h趋向于0) f(a+3h)-f(a-h) /h=?

这个可以用等价无穷小代换f(a+3h) = f(a) + (3h)*f'(a) + (3h)^2*f''(a)/2!+ ...f(a-h) = f(a) + (-h)*f'(a) + (h^2)f''(a)/2!+ .相减得f(a+3h)-f(a-h) = 4h * f'(a) + O(h^2)所以f(a+3h)-f(a-h) / h = 4*f'(a) = 4*...