Question

Solve:
$\underset{x\to 0}{lim}\left(\right[x^2]-[x{]}^2)$

Answer 1

We have,

$\underset{x\to 0}{lim}\left[x^2\right]-[x{]}^2$

Take R.H.L

$\underset{x\to 0^{+}}{lim}\left[x^2\right]-[x{]}^2$

$=\left[\right(0^{+}{)}^2]-[0^{+}{]}^2$

$=\left[0\right]-(0{)}^2$

$=0-0=0$

Take L.H.L

$\underset{x\to 0^{-}}{lim}\left[x^2\right]-[x{]}^2$

$=\left[\right(0^{-}{)}^2]-[0^{-}{]}^2$

$=\left[0\right]-(0{)}^2$

$=0-0=0$

$\underset{x\to 0}{lim}\left[x^2\right]-[x{]}^2$

$=\left[0^2\right]-[0{]}^2$

$=0-0=0$

Hence, this is the answer.