设a不等于0,x趋于正无穷大,求（x+a)/(x- - 知识问答

设a不等于0,x趋于正无穷大,求（x+a)/(x-a)的x次幂的极限

1个回答

lim[(x+a)/(x-a)]^x
=lim[1+2a/(x-a)]^x
=lim{[1+2a/(x-a)]^[(x-a)/2a]}^[2ax/(x-a)]
=lim e^[2ax/(x-a)]
=e^{lim[2ax/(x-a)]}
=e^(2a)

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