第1个回答 2017-10-23
以下趋于多少均省略，注意加上：
（5）lim2^n*sinx/2^n
＝lim x*sin(x/2^n)/[x/2^n]
=xlimsin(x/2^n)/(x/2^n)
=x*1=x
(7 )lim[sqr(1-cosx)]/x =lim根号2 *sin(x/2) /x
＝sqr2 *limsin(x/2)/(x/2) /2
=(根号2）/2
（1）lim(1+3/n)^(-n)
=lim[(1+1/(n/3))^(n/3)]^(-3)
=e^(-3)
(3) lim [(x+3)/(x+1)]^x
=lim[1+2/(x+1)]^x
=lim{[1+1/((x+1)/2)]^[(x+1)/2]}^2 / lim[1+2/(x+1)]
=e^2 /1
=e^2
(5)lim(1-2x)^(1/x)
=lim{{1+1/(-1/(2x)]}^(-1/(2x))}^(-2)
=e^(-2)
(7) lim(1+tanx)^cotx
=lim(1+1/cotx)^cotx
=e本回答被网友采纳