Let's do some calculus! (9)

Calculus Level 4

\[\displaystyle \lim_{x\to a}~{\dfrac{\displaystyle \int_{a}^{x}{f(x)} \,dx - \left(\dfrac{x-a}{2}\right)\left(f(x)+f(a)\right)}{{\left(x-a\right)}^{3}}} = 0\]

For the above equation to be true, the maximum degree of \(f(x)\) can be?


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