极限的计算题
2个回答
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(x+3)/(x+2)
=1 + 1/(x+2)
let
1/y = 1/(x+2)
lim(x->∞) [(x+3)/(x+2)]^x
=lim(x->∞) [1 + 1/(x+2)]^x
=lim(y->∞) (1 + 1/y)^(y-2)
=lim(y->∞) (1 + 1/y)^y
=e
=1 + 1/(x+2)
let
1/y = 1/(x+2)
lim(x->∞) [(x+3)/(x+2)]^x
=lim(x->∞) [1 + 1/(x+2)]^x
=lim(y->∞) (1 + 1/y)^(y-2)
=lim(y->∞) (1 + 1/y)^y
=e
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