For $f(x) = [x]^{2} - [x^{2}]$, what is the left-hand limit at $x = 2$?

Explanation

1. 01

   Just left of 2: $[x] = 1$, so $[x]^{2} = 1$; and $x^{2}$ is just below 4, so $[x^{2}] = 3$.

2. 02

   The left-hand limit is $1 - 3 = -2$.