lim(x→0)(1-cos2x)/(xsinx)的极限
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lim(x→0)(1-cos2x)/(xsinx)的极限
lim(x→0)(1-cos2x)/(xsinx)的极限
lim(x→0)(1-cos2x)/(xsinx)的极限
lim(x→0)(1-cos2x)/(xsinx)
=lim(x→0)(2(sinx)^2)/(xsinx)
=lim(x→0)(2sinx)/(x)
=2
1-cos2x=2sin^2(x)
lim(x→0)2sin^2(x)=2x^2
lim(x→0)xsinx=x^2
所以原式=2
cos2x=2cos^x-1=1-2sin^x
那么分子就等于2sin^x,又因为x→0,sinx/x=1,所以sinx=x
带入 结果为2
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