GIF with Limits.

Calculus Level 4

Let $f(x)$ be a non-constant real valued polynomial function such that at the point $a$ we have $f(a)^2+f'(a)^2=0$ . Find the value of

$\lim_{x \to a} \dfrac{f(x)}{f'(x)} \cdot \left\lfloor \dfrac{f'(x)}{f(x)} \right\rfloor$

Note: $f'(x) = \dfrac{d}{dx} f(x)$