lim x→0(tanx-x)/x^2sinx用洛必达法则解答

lim x→0(tanx-x)/x^2sinx用洛必达法则解答
lim x→0(tanx-x)/x^2sinx用洛必达法则解答

lim x→0(tanx-x)/x^2sinx用洛必达法则解答
lim(x->0)(tanx-x)/(x^2sinx）=lim(x->0)(sinx-xcosx)/((1/2)x^2sin2x)
=lim(x->0)(sinx-xcosx)'/((1/2)x^2sin2x)'
=lim(x->0)(cosx-cosx+xsinx)/(xsin2x+x^2cos2x)
=lim(x->0)(xsinx)/(xsin2x+x^2cos2x)
=lim(x->0)(1/(2cosx+(x/sinx)cos2x))
=1/3