Question

当x→0时，无穷小x-x²与x²-x³相比，哪一个是较高阶的无穷小？

Answer 1

lim(x-x²)/(x²-x³)=lim[x(1-x)]/[x²(1-x)]=lim(1/x)所以，x²-x³是高阶无穷小

Answer 2

解：x-0,2x-x^2-0-0=0 x-0,x^3-x^4-0^3-0^4=0-0=0 二者都是无穷小量， limx-0(2x-x^2)/(x^3-x^4) =x(2-x)/x^3(1-x) =(2-x)/x^2(1-x) =（2-x)/(1-x)x1/x^2 limx-0 (2-x)/(1-x)=2/1=2 limx-01/x^2, 换元法：令t=x^2,x-0,x^2-0^2=0 t-0,limt-0 1/t-..