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:

Vertebrates

Animals with a backbone or spinal column, which includes mammals, birds, reptiles, amphibians, and fish.

Thick Filament

A component of muscle fiber primarily made of myosin, responsible for muscle contraction.

Myosin

A type of motor protein found in muscle cells and other cell types, essential for muscle contraction and movement within cells.

Sarcomere

The basic unit of muscle fiber responsible for muscle contraction, consisting of actin and myosin filaments.