lim(x→-∞)[（√（x+2）(x+5)）+x]=__..根号下是（x+2）乘于(x+5) 后面加的x不在根号下_数学解答

lim(x→-∞)[（√（x+2）(x+5)）+x]=__.
.
根号下是（x+2）乘于(x+5) 后面加的x不在根号下

人气：312 ℃　时间：2020-06-04 16:50:10

解答

(x+2)(x+5)=(x+3.5)^2-2.25
(√（(x+2）(x+5)）-|x+3.5|)(√（(x+2）(x+5)）+|x+3.5|)=-2.25
lim(x→-∞)[（√（(x+2）(x+5)）-|x+3.5|]
=lim(x→-∞)[-2.25/[√（(x+2）(x+5)）+|x+3.5|)]]
=0
于是
lim(x→-∞)[（√（(x+2）(x+5)）+x]=-3.5