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Find the first three nonzero terms of the Maclaurin expansion of the given functions.$$f(x)=(2 x-1)^{2}$$

$\sin ^{2}(-1)+\frac{2 \sin (-2)}{1 !} x+\frac{8 \cos (-2)}{2 !} x^{2}$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 2

Mclaurin Series

Series

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Oh we want to find the first three non zero terms of the MacLaurin series expansion for the function after taxes? Two x minus one square. This question is child your understanding of how to utilize series expansion? Who functions as such? We appreciate we have MacLaurin series is to solve this problem, MacLaurin series states that F of X is equal to zero plus F prime zero X plus F double time zero, which is about to expire and so on. Where the term of F MacLaurin series is the derivative of F zero. By the way, N factorial times X to the app. Thus we have since our derivative rather since our function F x zero is negative, one squared equals one because at least two derivatives. So F one is two times two, X minus one times two equals eight, X minus four, F two is eight. All and after that are zero. So are MacLaurin series ends at the second derivative. Thus we have series one minus four X plus four X squared with no continuation afterwards.

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