（(5x-2）/(5x+2))^x,x趋于无穷的极
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解决时间 2021-01-17 02:44
- 提问者网友：暗中人
- 2021-01-16 02:22
（(5x-2）/(5x+2))^x,x趋于无穷的极
最佳答案
- 五星知识达人网友：未来江山和你
- 2021-01-16 03:15
(5x-2)/(5x+2) = 1 - 4/(5x+2)
let
1/y = 4/(5x+2)
lim(x->∞) [(5x-2)/(5x+2)]^x
=lim(x->∞) [ 1 - 4/(5x+2)]^x
=lim(y->∞) [ 1 - 1/y]^[(4y-2)/5]
=lim(y->∞) [ 1 - 1/y]^(4y/5)
=e^(-4/5)
let
1/y = 4/(5x+2)
lim(x->∞) [(5x-2)/(5x+2)]^x
=lim(x->∞) [ 1 - 4/(5x+2)]^x
=lim(y->∞) [ 1 - 1/y]^[(4y-2)/5]
=lim(y->∞) [ 1 - 1/y]^(4y/5)
=e^(-4/5)
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