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limsinx-tanx/sinx的3次方,x趋向0的极限
人气:405 ℃ 时间:2020-02-05 16:57:44
解答
lim(x->0) (sinx-tanx)/(sinx)^3(0/0)
=lim(x->0) (cosx-(secx)^2)/[3(sinx)^2.cosx]
=lim(x->0) [(cosx)^3-1 ]/[3(sinx)^2.(cosx)^3] (0/0)
=lim(x->0) [-3(cosx)^2. sinx ]/[3(-3(sinx)^3.(cosx)^2+2sinx(cosx)^4) ]
=lim(x->0) -1/[(-3(sinx)^2.+2(cosx)^2) ]
= -1/2
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