What is the fourth degree Taylor polynomial for $\cos \left(3 x^{2}\right)$ about x = 0?
A) $1-\frac{9}{2} x^{4}$
B) $1-\frac{3}{2} x^{4}$
C) $1-\frac{9}{2} x^{2}+\frac{27}{6} x^{3}-\frac{81}{24} x^{4}$
D) $x+\frac{3}{2} x^{2}-\frac{9}{6} x^{3}+\frac{27}{24} x^{4}$

Question

Quizplus · Accepted Answer

The fourth degree Taylor polynomial for a function $f(x)$ about $x = 0$ includes terms up to $x^4$. For $\cos(3x^2)$, the Taylor series expansion is $1 - \frac{(3x^2)^2}{2!} + \cdots$, which simplifies to $1 - \frac{9x^4}{2}$ for the terms up to $x^4$, matching option A.

What Is the Fourth Degree Taylor Polynomial For cos⁡(3x2)\cos \left(3 x^{2}\right)cos(3x2)

What Is the Fourth Degree Taylor Polynomial For $\cos \left(3 x^{2}\right)$