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求lim(x→0) [√(1+x^2)-1/(1-cosx)]
人气:145 ℃ 时间:2020-04-13 18:36:29
解答
分子有理化:
=lim(x→0)x^2/(1-cosx)(√(1+x^2)+1) (√(1+x^2)+1趋于2:
=(1/2)lim(x→0)x^2/(1-cosx) (罗比达法则:
=(1/2)lim(x→0)2x/sinx
=1
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