求解题思路! 10
2个回答
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lim(x→0)[xsinx/(1-cosx)]
=lim(x→0)[2xsin(x/2)cos(x/2)]/{2[sin(x/2)]^2}
=lim(x→0)[xcos(x/2)]/sin(x/2)
=2lim(x→0)[(x/2)cos(x/2)]/sin(x/2)
=2lim(x→0){cos(x/2)/[sin(x/2)/(x/2)]
=2lim(x→0)cos(x/2)/lim(x→0)[sin(x/2)/(x/2)]
=2×1÷1
=2
=lim(x→0)[2xsin(x/2)cos(x/2)]/{2[sin(x/2)]^2}
=lim(x→0)[xcos(x/2)]/sin(x/2)
=2lim(x→0)[(x/2)cos(x/2)]/sin(x/2)
=2lim(x→0){cos(x/2)/[sin(x/2)/(x/2)]
=2lim(x→0)cos(x/2)/lim(x→0)[sin(x/2)/(x/2)]
=2×1÷1
=2
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