lim(x→∞)(x–1/x+1)^x
答案:2 悬赏:20
解决时间 2021-01-09 23:47
- 提问者网友:孤凫
- 2021-01-09 15:50
lim(x→∞)(x–1/x+1)^x
最佳答案
- 二级知识专家网友:躲不过心动
- 2021-01-09 16:15
解:
lim [(x-1)/(x+1)]^x
x→∞
=lim [(x+1-2)/(x+1)]^x
x→∞
=lim [1+ (-2)/(x+1)]^x
x→∞
=lim {[1+ (-2)/(x+1)]^[(x+1)/(-2)]}⁻² /[1+ (-2)/(x+1)]
x→∞
=e⁻²/(1+0)
=e⁻²
lim [(x-1)/(x+1)]^x
x→∞
=lim [(x+1-2)/(x+1)]^x
x→∞
=lim [1+ (-2)/(x+1)]^x
x→∞
=lim {[1+ (-2)/(x+1)]^[(x+1)/(-2)]}⁻² /[1+ (-2)/(x+1)]
x→∞
=e⁻²/(1+0)
=e⁻²
全部回答
- 1楼网友:你哪知我潦倒为你
- 2021-01-09 16:33
利用求极限的特殊极限,lim(1+1/x)^x=e
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