Question

${\lim }_{x\to k}x-[x]$is where k is an integer, is equal to

• A. 1
• B. 0
• C. 3
• D. 2

Answer 1

Answer: (B)

${\lim }_{x\to k}(x-[x])$ does not exist
${\lim }_{x\to k-}x-[x]=k-[k-]=k-(k-1)=1$
${\lim }_{x\to k+}x-[x]=k-[k+]=k-k=0$