Question

高等数学求极限 微积分基础

这题极限怎么求

Answer 1

利用分子有理化。详解见图

Answer 2

let

y=1/x

y->0+

(1-y^3)^(1/3) = 1-(1/3)y^3 +o(y^3)

-1+(1-y^3)^(1/3) = -(1/3)y^3 +o(y^3)

lim(x->+∞) [ -x-(1-x^3)^(1/3) ]

=lim(y->0+) [ -1/y-(1-1/y^3)^(1/3) ]

=lim(y->0+) [ -1-(y^3-1)^(1/3) ] /y 

=lim(y->0+) [ -1+(1-y^3)^(1/3) ] /y 

=lim(y->0+)  -(1/3)y^3  /y 

=0

Answer 3