Question

Evaluate $\underset{x\to 2}{lim}\{x+{(x-\left[x\right])}^2\}$, where $\left[x\right]$ denotes greatest integer function.

• A. 1
• B. 0
• C. -1
• D. does not exist

Answer 1

Answer: (D)

does not exist

$[2+h]=2,[2-h]=1$

$R=\underset{h\to 0}{lim}\{2+h+{(2+h-2)}^2\}=2$

$L=\underset{h\to 0}{lim}\{2-h+{(2-h-1)}^2\}=3$

$R.H.S\ne L.H.S$

$\therefore$ limit does not exist.
Ans: D