lim (x-2/x+2)^x+2 x→∞ 请问这题求极限是怎样解,
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lim (x-2/x+2)^x+2 x→∞ 请问这题求极限是怎样解,
![lim (x-2/x+2)^x+2 x→∞ 请问这题求极限是怎样解,](/uploads/image/z/18135625-49-5.jpg?t=lim+%28x-2%2Fx%2B2%29%5Ex%2B2+x%E2%86%92%E2%88%9E+%E8%AF%B7%E9%97%AE%E8%BF%99%E9%A2%98%E6%B1%82%E6%9E%81%E9%99%90%E6%98%AF%E6%80%8E%E6%A0%B7%E8%A7%A3%2C)
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)
=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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