求下列极限lim趋于0(tanx-x)/(x^2sinx) 求救啊

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求下列极限lim趋于0(tanx-x)/(x^2sinx)求救啊求下列极限lim趋于0(tanx-x)/(x^2sinx)求救啊求下列极限lim趋于0(tanx-x)/(x^2sinx)求救啊原式=l

求下列极限lim趋于0(tanx-x)/(x^2sinx) 求救啊
求下列极限lim趋于0(tanx-x)/(x^2sinx) 求救啊

求下列极限lim趋于0(tanx-x)/(x^2sinx) 求救啊
原式=lim(x→0)(tanx-x)/x^3 (等价无穷小)
=lim(x→0)(1/cos^2(x)-1)/(3x^2) (洛必达法则)
=lim(x→0)sin^2(x)/(3x^3)*1/cos^2(x)
=1/3 (等价无穷小)