已知f(a)的导数=3 则lim(h趋向于0) f(a+3h)-f(a-h) /h=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 23:22:46
![已知f(a)的导数=3 则lim(h趋向于0) f(a+3h)-f(a-h) /h=?](/uploads/image/z/5349042-18-2.jpg?t=%E5%B7%B2%E7%9F%A5f%28a%29%E7%9A%84%E5%AF%BC%E6%95%B0%3D3+%E5%88%99lim%28h%E8%B6%8B%E5%90%91%E4%BA%8E0%EF%BC%89+f%28a%2B3h%29-f%28a-h%29+%2Fh%3D%3F)
已知f(a)的导数=3 则lim(h趋向于0) f(a+3h)-f(a-h) /h=?
已知f(a)的导数=3 则lim(h趋向于0) f(a+3h)-f(a-h) /h=?
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* 3 = 12