lim (x-2/x+2)^x+2 x→∞ 请问这题求极限是怎样解,

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/20 19:49:53

lim_{x→∞}[(x-2)/(x+2)]^(x+2)
=lim_{x→∞}[1-4/(x+2)]^(x+2)
=lim_{x→∞}[1-4/(x+2)]^[-(x+2)/4*(-4)]
=lim_{x→∞}{[1-4/(x+2)]^[-(x+2)/4]}^(-4)
=e^(-4)

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