Find the Taylor series for $$\(f(x)=\frac{1}{\sqrt{x}}\)$$ centered at $$\(x=4\)$$.
A.
\(\sum_{n=0}^{\infty}(-1)^{n} \frac{1 \cdot 3 \cdot 5 \cdots(2 n-1)}{2^{3 n+1} n!}(x-4)^{n}\)
B.
\(\sum_{n=0}^{\infty}(-1)^{n} \frac{1 \cdot 3 \cdot 5 \cdots(2 n+1)}{4^{n+1}}(x-4)^{n}\)
C.
\(\sum_{n=0}^{\infty} \frac{1}{2^{2 n+1} n} x^{n}\)
D.
\(\sum_{n=1}^{\infty}(-1)^{n} \frac{2 \cdot 4 \cdot 6 \cdots 2 n}{2^{3 n+1} n!}(x-4)^{n}\)
Exam No：AP Calculus Unit 10 Questions Set 2 Year：2024 Question No：37
Answer:
A
Knowledge points:
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
Solution:
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