求极限,要明细哦求极限（要明细哦）
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/25 04:34:52
求极限,要明细哦求极限（要明细哦）求极限,要明细哦求极限（要明细哦）求极限,要明细哦求极限（要明细哦）lim(x->∞)[(x+5)/(x+2)]^(x+3)=lim(x->∞)[1+3/(x+2)]
求极限,要明细哦求极限（要明细哦）
求极限,要明细哦
求极限（要明细哦）
求极限,要明细哦求极限（要明细哦）
lim(x->∞) [(x+5)/(x+2)] ^(x+3)
=lim(x->∞) [1+ 3/(x+2)] ^[(x+2)/3 * 3(x+3)/(x+2)]
=lim(x->∞) {[1+ 3/(x+2)] ^(x+2)/3 } ^ 3(x+3)/(x+2)
显然在x趋于∞的时候,
[1+ 3/(x+2)] ^(x+2)/3的极限值为e,
而3(x+3)/(x+2)的极限值为3,
所以
原极限
=lim(x->∞) {[1+ 3/(x+2)] ^(x+2)/3 } ^ 3(x+3)/(x+2)
=e^3