Taylor's Theorem

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HallsofIvy
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Yes. By the product rule, the derivative of each term contains two parts: the part where you are differentiating [itex]f^{(n)}(x)[/itex] and the part where you re differentiating [itex](b- x)^n[/itex]. The first part cancels the previous term and the second part cancels the next term.
 

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