Question

Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0?

• A. $sin\left(x^3\right)$
• B. $sin\left(x^2\right)$
• C. $cos\left(x^3\right)$
• D. $cos\left(x^2\right)$

Answer 1

The correct option is A $sin\left(x^3\right)$

$sin{x}^3=x^3-\frac{(x^3{)}^3}{3!}+\frac{(x^3{)}^5}{5!}.....$