搜搜做题作业网极限 (n→∞) lim[1+1/(3n)]^(4n-2)
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/07/20 19:26:42
极限 (n→∞) lim[1+1/(3n)]^(4n-2)
原式= (n→∞) lim{[1+1/(3n)]^(4n)}/ [1+1/(3n)]^2= (n→∞) lim[1+1/(3n)]^(2n)=2/3 请问是错在哪里了?
原式= (n→∞) lim{[1+1/(3n)]^(4n)}/ [1+1/(3n)]^2= (n→∞) lim[1+1/(3n)]^(2n)=2/3 请问是错在哪里了?
![极限 (n→∞) lim[1+1/(3n)]^(4n-2)](/uploads/image/z/3862390-22-0.jpg?t=%E6%9E%81%E9%99%90+%28n%E2%86%92%E2%88%9E%29+lim%5B1%2B1%2F%283n%29%5D%5E%284n-2%29)
2n怎么来的?指数是相减,不是相除
原式= lim(n→∞) lim{[1+1/(3n)]^[(3n)*(4n-2)/3n]
= lim(n→∞) lim{[1+1/(3n)]^(3n)}^[(4n-2)/3n]
=e^(4/3)
原式= lim(n→∞) lim{[1+1/(3n)]^[(3n)*(4n-2)/3n]
= lim(n→∞) lim{[1+1/(3n)]^(3n)}^[(4n-2)/3n]
=e^(4/3)
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