Find the Taylor Series Centered At $x=0$ (IEThe Maclaurin Series)for $\sin \left(x^{2}\right)$

question 6

Multiple Choice

Find the Taylor series centered at $x=0$ (i.e.the Maclaurin series) for $\sin \left(x^{2}\right)$ .

• A) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{4 i+3}}{(4 i+1) !}\)
• B) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{4 i+2}}{(2 i+1) !}\)
• C) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{4 i}}{(2 i) !}\)
• D) \(\sum_{i=0}^{\infty} \frac{(-1)^{i} x^{4 i+1}}{(4 i) !}\)

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Definitions:

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The process of assigning names or categories to objects, people, or phenomena, often influencing perception and behavior.

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The process or act of making someone less agitated, anxious, or excited.

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