lim(x^2-2)/x+5),x→∞求极限

题目

lim(x^2-2)/x+5),x→∞求极限

答案

(x^2-2)/(x+5)
=(x^2-25+23)/(x+5)
=(x^2-25)/(x+5)+23/(x+5)
=(x-5)+23/(x+5)
lim(x^2-2)/x+5)
=lim((x-5)+23/(x+5)),x→∞
=x
=∞
因此极限就是∞