高数，求抽象函数的极限题目

Question

高数，求抽象函数的极限题目图一图二是同样类型的题目，我没有理解为什么f(2t)和f(3t)分别等于1/2和3，解释一个就可以了，谢谢

Answer 1

lim(x->0) f(2x)/x =2 (0/0)
=>f(0)=0
lim(x->0) 2f'(2x) =2
=>f'(0) =1
lim(x->0) x/f(3x) (0/0)
=lim(x->0) 1/(3f'(3x))
=1/(3f'(0))
=1/3
------------------------
lim(x->0) f(3x)/x =3 (0/0)
=>f(0)=0
lim(x->0) 3f'(3x) =3
=>f'(0) =1
let y=1/(3x)
lim(x->∞) x.f(1/(3x))
=(1/3)lim(y->0) f(y)/ y (0/0)
=(1/3)lim(y->0) f'(y)
=(1/3)f'(0)
=1/3本回答被网友采纳