The third-degree Taylor polynomial $$\(P_{3}(x)\)$$ for $$\(\sin x\)$$ about $$\(\frac{\pi}{4}\)$$ is
A.
\(\frac{1}{\sqrt{2}}\left(\left(x-\frac{\pi}{4}\right)-\frac{1}{3!}\left(x-\frac{\pi}{4}\right)^{3}\right)\)
B.
\(\frac{1}{\sqrt{2}}\left(1+\left(x-\frac{\pi}{4}\right)-\frac{1}{2}\left(x-\frac{\pi}{4}\right)^{2}+\frac{1}{3!}\left(x-\frac{\pi}{4}\right)^{3}\right)\)
C.
\(\frac{1}{\sqrt{2}}\left(1+\left(x-\frac{\pi}{4}\right)-\frac{1}{2!}\left(x-\frac{\pi}{4}\right)^{2}-\frac{1}{3!}\left(x-\frac{\pi}{4}\right)^{3}\right)\)
D.
\(1+\left(x-\frac{\pi}{4}\right)-\frac{1}{2}\left(x-\frac{\pi}{4}\right)^{2}-\frac{1}{6}\left(x-\frac{\pi}{4}\right)^{3}\)
Exam No：AP Calculus Unit 10 Questions Set Year：2024 Question No：37
Answer:
C
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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