来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 11:37:48
会的来 难题
会的来
难题
会的来 难题
7、
lim[(x+1)/x]^2x
=lim{[1+(1/x)]^x}^2
=e^2
8、
lim[1-(1/x)]^x
=lim{[1+(-1/x)]^(-x)}^(-1)
=e^(-1)
=1/e
1、
lim(1-cos2x)/(xsinx)
=lim[1-(1-2sin^2 x)]/(xsinx)
=lim(2sin^2 x)/(xsinx)
=2lim(sinx)/x
=2
2、
lim(tanx)^tan2x
=lim[1+(tanx-1)]^tan2x
=lim{[1+(tanx-1)]^[1/(tanx-1)]}^[(tanx-1)*tan2x]
=e^lim[(tanx-1)*tan2x]
=e^lim(tanx-1)*[2tanx/(1-tan^2 x)]
=e^lim(-2tanx)/(1+tanx)
=1/e
3、
lim[(x+a)/(x-a)]^x
=lim[(x-a+2a)/(x-a)]^x
=lim[1+(2a/x-a)]^x
=lim{[1+(2a/x-a)]^(x-a/2a)}^[2ax/(x-a)]
=e^lim[2ax/(x-a)]
=e^lim2a/[1-(a/x)]
=e^2a
4、
lim[√(n^2+1)/(n+1)]^n
=lim{1+[√(n^2+1)-(n+1)]/(n+1)}^n
=……【中间过程同上面③】
=1/e
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