Question

当x→1时,无穷小1－x和1－x的1/3次幂是否同阶?是否等价?

Answer 1

lim(x->1) (1-x)/(1-x^(1/3))

=lim(x->1) (1-x)(1+x^(1/3)+x^(2/3))/(1-x^(1/3))(1+x^(1/3)+x^(2/3))

=lim(x->1) (1-x)(1+x^(1/3)+x^(2/3))/(1-x)

=lim(x->1) (1+x^(1/3)+x^(2/3))

=1+1+1

=3

所以

同阶但不等价.