lim(x→0)(1-cos2x)/xsinx

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lim(x→0)(1-cos2x)/xsinx

lim(x→0)(1-cos2x)/xsinx
lim(x→0)(1-cos2x)/xsinx

lim(x→0)(1-cos2x)/xsinx
1-cos2x=2sin²x
(1-cos2x)/xsinx =2sinx/x
lim(x→0)=2lim(x→0)sinx/x =2

lim(x→0)(1-cos2x)/xsinx=lim(x→0)(1-cosx平方+sinx平方)/xsinx
=lim(x→0)2sinx平方/xsinx
=lim(x→0)2sinx/x
然后用洛必达 =2lim(x→0) (sinx)'/x'
=2lim(x→0) cosx
=2

上下分别求导 lim(x-0)2sin2x/(sinx+xcosx)
把x=0带入cosx 上下分别求导 lim(x-0)4cos2x/(cosx+1)
把x=0带入 4/(1+1)=2