009C Sample Final 2, Problem 8

Find $n$ such that the Maclaurin polynomial of degree $n$ of $f(x)=\cos(x)$ approximates $\cos {\frac {\pi }{3}}$ within 0.0001 of the actual value.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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