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?_数学解答

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?

人气：450 ℃　时间：2020-03-31 01:59:33

解答

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.