大学数学 极限问题（急）
kuaidi.ping-jia.net 作者：佚名 更新日期：2024-06-17
大学数学极限问题
(1)原式等于
lim[1-2/(x+1)]^{[-(x+1)/2]*[-2x/(x+1)]}
=lim{[1-2/(x+1)]^{[-(x+1)/2]}^[-2x/(x+1)]
=e^lim[-2x/(x+1)]
=e^{-2lim[x/(x+1)]}
=(1/e^2)^lim[1-1/(x+1)]
=1/e^2
(2)原式等于
lim[1/(x-1)-2/(x^2-1)]
=lim[(x+1)/(x^2-1)-2/(x^2-1)]
=lim{(x-1)/[(x+1)(x-1)]}
=lim1/(x+1)
=1/2
g.e. = 2*lim{[3+(5/x²)]/[5+(3/x)]}[sin(2/x)/(2/x)]
= 2*(3/5)*1
= 6/5。
(1)原式等于
lim[1-2/(x+1)]^{[-(x+1)/2]*[-2x/(x+1)]}
=lim{[1-2/(x+1)]^{[-(x+1)/2]}^[-2x/(x+1)]
=e^lim[-2x/(x+1)]
=e^{-2lim[x/(x+1)]}
=(1/e^2)^lim[1-1/(x+1)]
=1/e^2
(2)原式等于
lim[1/(x-1)-2/(x^2-1)]
=lim[(x+1)/(x^2-1)-2/(x^2-1)]
=lim{(x-1)/[(x+1)(x-1)]}
=lim1/(x+1)
=1/2
