Question

學測數學只有前標但想要數甲頂標的認真人

第一題跟第二題差在哪

(+2)
類題 34 設n為整數,求:(1) lim(x-[x])
x-n
(1) lim (X-[x]) =)
xin
(2)
(2) lim[x-[x]] =
x-n
Ø
O

Answer 1

qn

左極限：
lim ( x-[x] ) = lim (x-n+1) = 1
lim [ x-[x] ] = lim [x-n+1] = lim 0 = 0
↑ ↑
∵n-1<x<n ∵n-1<x<n
∴[x]=n-1 ∴[x-n+1]=0
右極限：
lim ( x-[x] ) = lim (x-n) = 0
lim [ x-[x] ] = lim [x-n] = lim 0 = 0
↑ ↑
∵n<x<n+1 ∵n<x<n+1
∴[x]=n ∴[x-n]=0