Question

For $\underset{x\to 2}{lim}{x}^2-[x{]}^2$, which of the following is/are correct?
([.] denotes greatest integer function)

• A. The right hand limit is $0.$
• B. The left hand limit is $3.$
• C. The left hand limit is $0.$
• D. The right hand limit is $3.$

Answer 1

Answer: (A), (B)

The left hand limit is $3.$

Given : $\underset{x\to 2}{lim}{x}^2-[x{]}^2$
Finding L.H.L and R.H.L.
L.H.L.
$\underset{x\to 2^{-}}{lim}{x}^2-[x{]}^2=4-1=3$
R.H.L.
$\underset{x\to 2^{+}}{lim}{x}^2-[x{]}^2=4-4=0$