求极限lim(x->0) 1/x^3 {[(2+cosx)/3]^x-1}求极限lim(x->0)1/x^3 {[(2+cosx)/3]^x-1}

来源：学生作业帮助网编辑：作业帮时间：2024/05/01 17:03:05

$求极限lim(x->0) 1/x^3 {[(2+cosx)/3]^x-1}求极限lim(x->0)1/x^3 {[(2+cosx)/3]^x-1}$

求极限lim(x->0) 1/x^3 {[(2+cosx)/3]^x-1}求极限lim(x->0)1/x^3 {[(2+cosx)/3]^x-1}
求极限lim(x->0) 1/x^3 {[(2+cosx)/3]^x-1}
求极限lim(x->0)
1/x^3 {[(2+cosx)/3]^x-1}

求极限lim(x->0) 1/x^3 {[(2+cosx)/3]^x-1}求极限lim(x->0)1/x^3 {[(2+cosx)/3]^x-1}
=1/x^3{e^[ln((2+cosx)-ln3)*x]-1} e^x~1+x
=1/x^3[ln((2+cosx)-ln3)*x] ln(1+x)~x
=1/x^2[(2+cosx)/3-1]
=1/x^2[(cosx-1)/3]
=1/x^2(-2sin^2(x/2))/3
=-2/3*(1/2)^2
=-1/6

我就知道你这厮会采用这种方法

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