009C Sample Final 1, Problem 6

Find the Taylor polynomial of degree 4 of $f(x)=\cos ^{2}x$ at $a={\frac {\pi }{4}}$.

Foundations:

Solution:

Step 1:
First, we make a table to find the coefficients of the Taylor polynomial.
$n$ $f^{(n)}(x)$ $f^{(n)}(a)$ ${\frac {f^{(n)}(a)}{n!}}$ $0$ $1$ $2$ $3$ $4$

Step 2:

Final Answer:

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