数学求极限问题

第一步后就不理解了
2025-05-06 15:34:28
推荐回答(1个)
回答1:

lim(x->0) [x^2.f(x) -2f(x^3)]/x^3 (0/0)
分子,分母分别求导
=lim(x->0) [2x.f(x)+x^2.f'(x) -6x^2.f'(x^3)]/(3x^2)
=lim(x->0) [2f(x)+xf'(x) -6xf'(x^3)]/(3x)
=lim(x->0) 2f(x)/(3x) + lim(x->0)[f'(x) -6f'(x^3)]/3
=(2/3){ lim(x->0) [f(x)-f(0)]/x } + [f'(0) -6f'(0)]/3
=(2/3)f'(0) - (5/3)f'(0)
=-f'(0)