lim(cos1/n)^n^2 n->∞
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/09 00:54:23
lim(cos1/n)^n^2 n->∞
lim (1+|x|)^1/x x->0
lim (1+|x|)^1/x x->0
cos2X=1-2*(sinX)^2
lim(cos1/n)^n^2
=lim[(1-2sin^2(1/2n))^(-1/2sin^2(1/2n))]^[n^2*2sin^2(1/2n))]
=e^lim[n^2*2sin^2(1/2n))]
=e^(1/2)
lim (1+|x|)^1/x x->0
x>0且 x->0 lim (1+|x|)^1/x=e
x0 lim (1+|x|)^1/x=e^(-1)=1/e
故lim (1+|x|)^1/x x->0极限不存在
lim(cos1/n)^n^2
=lim[(1-2sin^2(1/2n))^(-1/2sin^2(1/2n))]^[n^2*2sin^2(1/2n))]
=e^lim[n^2*2sin^2(1/2n))]
=e^(1/2)
lim (1+|x|)^1/x x->0
x>0且 x->0 lim (1+|x|)^1/x=e
x0 lim (1+|x|)^1/x=e^(-1)=1/e
故lim (1+|x|)^1/x x->0极限不存在
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