limx趋近于0sin2x/sin5x

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limx趋近于0sin2x/sin5xlimx趋近于0sin2x/sin5xlimx趋近于0sin2x/sin5x应用等阶无穷小因为当x->0时,sin2x与2x等阶,sin5x与5x等阶.故lim(

limx趋近于0sin2x/sin5x
limx趋近于0sin2x/sin5x

limx趋近于0sin2x/sin5x
应用等阶无穷小
因为当x->0时,sin2x与2x等阶,sin5x与5x等阶.
故lim(sin2x/sin5x)
=lim2x/5x
=2/5

x趋于0时sinx和x是等价无穷小
所以原式=lim(x趋于0)2x/5x=2/5