limit x->∞ [(x^3+2x)^1/3] / (x^2+1)
感謝
limitx>∞[(x^3+2x)^1/3]/(x^2+1)
2012-11-10 10:01 am
回答 (1)
2012-11-10 3:47 pm
✔ 最佳答案
[(x^3 + 2x)^(1/3)]/(x^2 + 1) = [x^3(1 + 2/x2)]^(1/3)]/[x^2(1 + 1/x^2)]= [x(1 + 2/x2)^(1/3)]/[x^2(1 + 1/x^2)]
= (1 + 2/x^2)^(1/3)/[x(1 + 1/x^2)
When x tends to infinity, 2/x^2 and 1/x^2 tends to zero, the expression becomes 1/x. So limit tends to infinity is zero.
收錄日期: 2021-04-13 19:05:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20121110000051KK00049