比较下面无穷小量的阶：当X--->0+时,根号下（x的3次方+根号下x）与tanx

Question

比较下面无穷小量的阶：当X--->0+时,根号下（x的3次方+根号下x）与tan x

Answer 1

lim(x→0+）√（x^3+√x）/tan x
=lim(x→0+）√（x^3+√x）/ x
=lim(x→0+）√[（x^3+√x）/ x^2]
=lim(x→0+）√[x+√x/ x^2]
=∞