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Let f(x)f(x)f(x) be a non-constant real valued polynomial function such that at the point aaa we have f(a)2+f′(a)2=0f(a)^2+f'(a)^2=0f(a)2+f′(a)2=0. Find the value of
limx→af(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\rfloorx→alimf′(x)f(x)⋅⌊f(x)f′(x)⌋
Note: f′(x)=ddxf(x)f'(x) = \dfrac{d}{dx} f(x)f′(x)=dxdf(x)
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