求极限limxsin2x/x^2+1,x为趋向无穷

问题描述:

求极限limxsin2x/x^2+1,x为趋向无穷

答:
lim(x→∞) xsin2x/(x^2+1)
=lim(x→∞) sin2x/(x+1/x)
=lim(x→∞) sin2x/x
=0
(因为:sin2x总是有界,属于[-1,1],而x是无穷)

答案给的结果是2

晕倒,你把题目编辑好......不要少括号答:lim(x→∞) xsin[2x/(x^2+1)]=lim(x→∞) xsin[2/(x+1/x)]=lim(x→∞) xsin(2/x) =lim(x→∞) 2sin(2/x) /(2/x)=2嘿嘿,不好意思哈,谢了请采纳支持,谢谢