作业帮求此式子的极限
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 03:54:06
求此式子的极限
求此式子的极限
求此式子的极限
这是1^∞型极限,使用重要极限lim(x→∞) [1+(1/x)]^x=e
lim(x→∞) [(x-1)/(x+3)]^(x+2)
=lim(x→∞) [1-4/(x+3)]^(x+2)
=lim(x→∞) [1-4/(x+3)]^{[-(x+3)/4]*[-4(x+2)/(x+3)]}
=lim(x→∞) {[1-4/(x+3)]^[-(x+3)/4]}^[-4(x+2)/(x+3)]
=e^lim(x→∞)[-4(x+2)/(x+3)]
=e^lim(x→∞)[-4(1+2/x)/(1+3/x)]
=e^(-4)