Question

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

Answer 1

Answer: 3

$\underset{x\to 2^{-}}{\lim }\left\{x+(x-[x]{)}^2\right\}=\underset{x\to 2^{-}}{\lim }\left\{x+(x-1{)}^2\right\}$
$=\underset{x\to 2^{-}}{\lim }\left(x^2-x+1\right)$
$=4-2+1=3$