x趋近于0 x的1⼀3次方+x的3⼀4次方是x的几阶无穷小?

2025-04-13 17:25:44
推荐回答(1个)
回答1:

x趋近于0时 x^(1/3)+x^(3/4)是x的几阶无穷小?
解:由于x➔0lim[(x^(1/3)+x^(3/4)]/x^(1/3)]=x➔0lim{x^(1/3)[1+x^(5/12)]/x^(1/3)}
=x➔0lim[1+x^(5/12)]=1,∴x➔0时x^(1/3)+x^(3/4)是x的1/3阶无穷小。或者说x^(1/3)+x^(3/4)与
x^(1/3)是等价的无穷小。