如图，求极限
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(x-1)/(x+1) = 1 - 2/(x+1)
let
2/(x+1) = 1/y
lim(x->∞) [(x-1)/(x+1)]^x
=lim(x->∞) [1 - 2/(x+1)]^x
=lim(y->∞) (1 - 1/y )^(2y-1)
=lim(y->∞) (1 - 1/y )^(2y)
=e^(-2)
let
2/(x+1) = 1/y
lim(x->∞) [(x-1)/(x+1)]^x
=lim(x->∞) [1 - 2/(x+1)]^x
=lim(y->∞) (1 - 1/y )^(2y-1)
=lim(y->∞) (1 - 1/y )^(2y)
=e^(-2)
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