Let \( f \) be a differentiable function satisfying the relation \( f(x+y)=f(x)+f(y)-2 x y+\left...

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Let \( f \) be a differentiable function satisfying the relation \( f(x+y)=f(x)+f(y)-2 x y+\left(e^{x}-1\right)\left(e^{y}-1\right) \forall x, y \in R \) and \( f^{\prime}(0)=1 \). The value of \( \lim _{x \rightarrow 0} \frac{f(2 x)+4 x^{2}-2 x}{x^{2}} \) is:
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