求极限lim(x→+∞)[(x+3)/(x+2)]^x,要具体过程,

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 05:17:53
求极限lim(x→+∞)[(x+3)/(x+2)]^x,要具体过程,

求极限lim(x→+∞)[(x+3)/(x+2)]^x,要具体过程,
求极限lim(x→+∞)[(x+3)/(x+2)]^x,要具体过程,

求极限lim(x→+∞)[(x+3)/(x+2)]^x,要具体过程,
lim(x->∞) [(x+3)/(x+2)]^x
= lim(x->∞) [((x+2)+1)/(x+2)]^x
= lim(x->∞) [1 + 1/(x+2)]^x
= lim(x->∞) [1 + 1/(x+2)]^[(x+2) * x/(x+2)]
= e^lim(x->∞) x/(x+2)
= e^lim(x->∞) 1/(1+2/x)
= e^[1/(1+0)]
= e

lim(x->+∞)[(x+3)/(x+2)]^x
=lim(x->+∞)[1 + 1/(x+3)]^x
=e