Find the Taylor series for $$\(f(x)=\cos (\pi x)\)$$ centered at $$\(x=3\)$$.
A.
\(\sum_{n=0}^{\infty} \frac{(-1)^{n} \pi^{2 n-2}}{(2 n)!}(x-1)^{2 n}\)
B.
\(\sum_{n=0}^{\infty} \frac{(-1)^{n+1} \pi^{2 n}}{(2 n)!}(x-1)^{2 n}\)
C.
\(\sum_{n=0}^{\infty} \frac{\pi^{2 n-1}}{(2 n-1)!} x^{2 n-1}\)
D.
\(\sum_{n=0}^{\infty} \frac{(-1)^{n+1}}{n!\pi^{2 n}}(x-1)^{n}\)
Exam No：AP Calculus Unit 10 Questions Set 2 Year：2024 Question No：38
Answer:
B
Knowledge points:
10.11 Finding Taylor Polynomial Approximations of Functions
10.14 Finding Taylor or Maclaurin Series for a Function
Solution:
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