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AP Calculus BC/Unit 10: Infinite Sequences and Series
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Taylor Polynomial Formula

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Which of the following represents the Taylor polynomial of degree nn for a function ff centered at x=ax=a?

A

Pn(x)=f(a)+f′(a)(x−a)+f′′(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)nP_n(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x - a)^n

B

Pn(x)=f(a)+f′(a)x+f′′(a)2!x2+⋯+f(n)(a)n!xnP_n(x) = f(a) + f'(a)x + \frac{f''(a)}{2!}x^2 + \cdots + \frac{f^{(n)}(a)}{n!}x^n

C

Pn(x)=f(x)+f′(x)(x−a)+f′′(x)2!(x−a)2+⋯+f(n)(x)n!(x−a)nP_n(x) = f(x) + f'(x)(x - a) + \frac{f''(x)}{2!}(x - a)^2 + \cdots + \frac{f^{(n)}(x)}{n!}(x - a)^n

D

Pn(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+⋯+f(n)(a)n(x−a)nP_n(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2}(x - a)^2 + \cdots + \frac{f^{(n)}(a)}{n}(x - a)^n

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