lim(x→∞)(x-5/x+3)∧x的极限怎么求 谢谢
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解决时间 2021-01-14 20:15
- 提问者网友：骑士
- 2021-01-13 20:50
lim(x→∞)(x-5/x+3)∧x的极限怎么求 谢谢
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- 二级知识专家网友：鸽屿
- 2021-01-13 22:01
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- 1楼网友：行路难
- 2021-01-13 22:56
lim(x→∞)[(x-5)/(x+3)]^x
=lim(x→∞)[(x+3-8)/(x+3)]^x
=lim(x→∞)[1-8/(x+3)]^x
=lim(x→∞)[1-8/(x+3)]^(x+3-3)
=lim(x→∞)[1-8/(x+3)]^(x+3)*[1-8/(x+3)]^(-3)
=lim(x→∞)[1-8/(x+3)]^(x+3)
=lim(x→∞){[1-8/(x+3)]^(x+3)/8}^8
=e^-8
=lim(x→∞)[(x+3-8)/(x+3)]^x
=lim(x→∞)[1-8/(x+3)]^x
=lim(x→∞)[1-8/(x+3)]^(x+3-3)
=lim(x→∞)[1-8/(x+3)]^(x+3)*[1-8/(x+3)]^(-3)
=lim(x→∞)[1-8/(x+3)]^(x+3)
=lim(x→∞){[1-8/(x+3)]^(x+3)/8}^8
=e^-8
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