求极限lim(x趋向于0) (x-tanx)/xsinx^2
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求极限lim(x趋向于0) (x-tanx)/xsinx^2
lim(x-tanx)/xsinx^2
=lim(x-tanx)/(x * x^2 * sinx^2 / x^2) 等价无穷小量:
=lim(x-tanx)/(x * x^2)
=lim(1/x^2 - sinx/x * 1/[x^2 * (cosx)]
=lim(1 - secx)/x^2 罗必塔法则:
=lim(-tanxsecx)/2x 罗必塔法则:
=-1/2limsecx(tan^2 x + sec^2 x)
=-1/2
再问: 我觉得你第三个等号时算错了,请修改...
再答: 没算错啊,lim(x-tanx)/(x * x^2)=lim1/x^2 - sinx/x * 1/(x^2 * cosx)把tanx=sinx/cosx
再问: 我只算到(xcosx-sinx)/x^2*cosx,算不到你的第三个=号那条式,请讲解一下
再答: (x-tanx)/(x * x^2) =x/(x * x^2) - tanx/(x * x^2) =1/x^2 - (sinx/cosx)/(x * x^2) =1/x^2 - sinx/x * 1/(cosx * x^2)
=lim(x-tanx)/(x * x^2 * sinx^2 / x^2) 等价无穷小量:
=lim(x-tanx)/(x * x^2)
=lim(1/x^2 - sinx/x * 1/[x^2 * (cosx)]
=lim(1 - secx)/x^2 罗必塔法则:
=lim(-tanxsecx)/2x 罗必塔法则:
=-1/2limsecx(tan^2 x + sec^2 x)
=-1/2
再问: 我觉得你第三个等号时算错了,请修改...
再答: 没算错啊,lim(x-tanx)/(x * x^2)=lim1/x^2 - sinx/x * 1/(x^2 * cosx)把tanx=sinx/cosx
再问: 我只算到(xcosx-sinx)/x^2*cosx,算不到你的第三个=号那条式,请讲解一下
再答: (x-tanx)/(x * x^2) =x/(x * x^2) - tanx/(x * x^2) =1/x^2 - (sinx/cosx)/(x * x^2) =1/x^2 - sinx/x * 1/(cosx * x^2)
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