Which of the following expresses the th-degree Taylor polynomial of a differentiable…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Which of the following expresses the

n

th-degree Taylor polynomial

P_n(x)

of a differentiable function

f

about

x=a

? (a)

P_n(x)=\displaystyle\sum_{k=0}^{n} f^{(k)}(a)(x-a)^k

(b)

P_n(x)=\displaystyle\sum_{k=0}^{n}\dfrac{f^{(k)}(a)}{k!}x^k

(c)

P_n(x)=\displaystyle\sum_{k=0}^{n}\dfrac{f^{(k)}(a)}{k!}(x-a)^k

(d)

P_n(x)=f(a)+\displaystyle\sum_{k=1}^{n}\dfrac{f^{(k)}(a)}{k}(x-a)^k