APFIVE Taylor Polynomial Formula
Which of the following represents the Taylor polynomial of degree $$n$$ for a function $$f$$ centered at $$x=a$$?
A
$$P_n(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x - a)^n$$
B
$$P_n(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2}(x - a)^2 + \cdots + \frac{f^{(n)}(a)}{n}(x - a)^n$$
C
$$P_n(x) = f(x) + f'(x)(x - a) + \frac{f''(x)}{2!}(x - a)^2 + \cdots + \frac{f^{(n)}(x)}{n!}(x - a)^n$$
D
$$P_n(x) = f(a) + f'(a)x + \frac{f''(a)}{2!}x^2 + \cdots + \frac{f^{(n)}(a)}{n!}x^n$$