Actually
lim(x→∞) (3^x+4^x+5^x)^(1/x) = 5
lim(x→-∞) (3^x+4^x+5^x)^(1/x) = 3
But Why?
Solve Limits lim(x→±∞) (3^x+4^x+5^x)^(1/x) = ?
2017-05-25 8:42 pm
回答 (1)
2017-05-25 9:27 pm
✔ 最佳答案
Sollim(x→∞)_(3^x+4^x+5^x)^(1/x)
=lim(x→∞)_｛ [(3/5)^x+(4/5)^x+(5/5)^x]*5^x｝^(1/x)
=lim(x→∞)_(5^x)^(1/x)
=5
lim(x→－∞)_(3^x+4^x+5^x)^(1/x)
=lim(x→－∞)_[(3/3)^x+(4/3)^x+(5/3)^x]^(1/x)
=lim(x→－∞)_｛[(3/3)^x+(4/3)^x+(5/3)^x]*(3^x)｝^(1/x)
=lim(x→－∞)_[(1+0+0)*(3^x)]^(1/x)
=3
收錄日期: 2021-04-30 22:03:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170525124225AAVjk1L