lim[(x-tanx)/x^2sinx](x趋向于0)用洛必达法则
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![lim[(x-tanx)/x^2sinx](x趋向于0)用洛必达法则](/uploads/image/z/2622371-59-1.jpg?t=lim%5B%28x-tanx%29%2Fx%5E2sinx%5D%28x%E8%B6%8B%E5%90%91%E4%BA%8E0%29%E7%94%A8%E6%B4%9B%E5%BF%85%E8%BE%BE%E6%B3%95%E5%88%99)
lim[(x-tanx)/x^2sinx](x趋向于0)用洛必达法则
lim[(x-tanx)/x^2sinx](x趋向于0)用洛必达法则
lim[(x-tanx)/x^2sinx](x趋向于0)用洛必达法则
lim(x→0)[(x-tanx)/x^2sinx] (用等价无穷小代换)
=lim(x→0)(x-tanx)/x^3 (0/0,用洛必达法则)
=lim(x→0)(1-sec^2x)/(3x^2)
=lim(x→0)-tan^2x/(3x^2) (用等价无穷小代换)
=lim(x→0)-x^2/(3x^2)
=-1/3
=lim[(x-tanx)/x^3]=lim[1-secx^2/3x^2]=lim[-tanx^2/3x^2]=lim[-x^2/3x^2]=-1/3
答案是-1/3 你的答案错了