求极限limx→0(x-sin2x/x+sin5x)

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求极限limx→0(x-sin2x/x+sin5x)求极限limx→0(x-sin2x/x+sin5x)求极限limx→0(x-sin2x/x+sin5x)原式=lim[(1-sin2x/x)/(1+

求极限limx→0(x-sin2x/x+sin5x)
求极限limx→0(x-sin2x/x+sin5x)

求极限limx→0(x-sin2x/x+sin5x)
原式
=lim[(1-sin2x/x)/(1+sin5x/x)]
=lim[(1-sin2x/(2x)*2)/(1+sin5x/(5x)*5)]
=[(1-lim(sin2x/(2x))*2)/(1+lim(sin5x/(5x))*5)]
=(1-2)/(1+5)
=-1/6