# Limits Plus: IV

Calculus Level 3

Suppose $$f$$ is a function that satisfies the equation

$$f(x+y)=f(x)+f(y)+x^2y+xy^2$$

for all real numbers $$x$$ and $$y$$. Suppose also that

$$lim_{x\rightarrow 0}{\frac{f(x)}{x}}=1$$.

Evaluate $$f(0)+f'(0)+f'(x)-x^2$$.

NOTE: No L'Hôpital's Rule is allowed.

Problem credit: Calculus: 6E, James Stewart

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