lim (x->infinity) [√(x+1) (√(x+2)- √x)]
lim (x->infinity) {1/[√(x^2+5)-√(x^2+x)]}
M2 math limit
2011-01-16 2:10 am
回答 (1)
2011-01-16 2:30 am
✔ 最佳答案
lim (x->∞) [√(x+1) (√(x+2)- √x)]= lim (x->∞) [2√(x+1)/(√(x+2)+ √x)]= lim (x->∞) [2√(1+1/x)/(√(1+2/x)+ 1)]= 2/2= 1lim (x->∞) {1/[√(x^2+5)-√(x^2+x)]}= lim (x->∞) [√(x^2+5)+√(x^2+x)]/(5-x)= lim (x->∞) [√(1+5/x^2)+√(1 + 1/x)]/(5/x - 1)= -(1 + 1)= -2
收錄日期: 2021-04-26 14:03:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110115000051KK00940