Find $\lim_{x \to 2^+} \frac{\lfloor x^2 \rfloor - \lfloor x \rfloor^2}{x^2 - 4}$

Question

How to find $\lim_{x \to 2^+} \frac{\lfloor x^2 \rfloor - \lfloor x \rfloor^2}{x^2 - 4}$

My textbook says limit doesn't exist but graph says it's zero.

Answer 1

The graph is correct. If $x$ is just above 2, the numerator is 4-4=0, and the denominator isn't.