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

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

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

lim(x^2*sinx-2x^3)/(x^3+2x^4)
=lim(sinx-2x)/(x+2x^2)
0/0型
上下分别求导
=lim(cosx-2)/(1+4x)
=(1-2)/(1+0)
=-1

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

=lim(-x^3)/(x^3+2x^4)
=lim(-1)/(1+2x)
=-1