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

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