GIF with Limits.

Calculus Level 4

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

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

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

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