求极限：lim(x^2*sinx-2x^3)/(x^3+2x^4) 当x趋向于0

题目

求极限：lim(x^2*sinx-2x^3)/(x^3+2x^4) 当x趋向于0

答案

lim(x→0) (x^2*sinx-2x^3)/(x^3+2x^4)
=lim(x→0) (sinx-2x)/(x+2x^2) (0/0)
= lim(x→0) (cosx-2)/(1+2x)
=-1