这个极限为什么等于零?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/05/29 17:58:17
这个极限为什么等于零?
多次利用洛必达法则可
lim(n→∞)(n^2)/[e^(√n)]
= lim(x→∞)(x^4)/(e^x) (∞/∞)
= lim(x→∞)4(x^3)/(e^x) (∞/∞)
= lim(x→∞)4*3(x^2)/(e^x) (∞/∞)
= lim(x→∞)4*3*2x/(e^x) (∞/∞)
= 4!*lim(x→∞)[1/(e^x)]
= 0
lim(n→∞)(n^2)/[e^(√n)]
= lim(x→∞)(x^4)/(e^x) (∞/∞)
= lim(x→∞)4(x^3)/(e^x) (∞/∞)
= lim(x→∞)4*3(x^2)/(e^x) (∞/∞)
= lim(x→∞)4*3*2x/(e^x) (∞/∞)
= 4!*lim(x→∞)[1/(e^x)]
= 0