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Find the first three nonzero terms of the Maclaurin expansion of the given functions.$$f(x)=\cos ^{2} x$$

$1-x^{2}+\frac{1}{3} x^{4}-\frac{2}{45} x^{6}$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 2

Mclaurin Series

Series

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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uh huh. We want to find the first three non zero terms of the MacLaurin series. Four, F X. Is equal to the cosine squared effects. This question is testing our knowledge of MacLaurin series. Remember the MacLaurin series states that F of X is equal to F of zero plus F prime zero X plus X double prime 0/2 sexual X squared plus F 3 0/3 sexual X cubed and so on. That is every editor. But over the MacLaurin series is the derivative of F zero divided by n factorial times extra. The fx equals coast squared X is one at zero. Therefore we have to find at least two derivatives on zero terms. F one is negative two coastline X. Synnex since sine of zero is zero at front, one is zero. F two is two. sine squared x mitsuko squared x. The sign goes to zero but the negative to co squared X evaluates to negative two. F four similarly zero rather F three similarly has a cenex, multiply it zero, but F four also gives us another term. So from F F two and F four, we can evaluate our series by politicians, MacLaurin series S one minus X squared plus one third x fourth, repeating.

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