Solve Maclaurin Expansion Equation: cos(x)-2x2=0

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Homework Help Overview

The discussion revolves around using the Maclaurin series expansion of the cosine function to solve the equation cos(x) - 2x² = 0. Participants are exploring the accuracy of their approximations and calculations within the context of this mathematical problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the initial attempt to use the first two terms of the Maclaurin series for cos(x) and question whether this approach is sufficient. There is a clarification sought regarding the meaning of "non-vanishing" terms in the series expansion.

Discussion Status

The conversation is ongoing, with participants sharing their findings and questioning the accuracy of their results. Some guidance has been provided regarding the need to consider higher-order terms in the expansion, and there is an acknowledgment of the difference between calculated and actual values.

Contextual Notes

Participants note that this is an exam practice question, which may influence their approach and the rigor of their solutions. There is also mention of checking accuracy with a calculator, indicating a desire to validate their findings.

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Homework Statement


Use the first two terms of the Maclaurin series expansion of cos(x) to solve the equation cos(x)-2x2=0 . Check its accuracy with a calculator ( is in radians).


Homework Equations



f(x)=f(0)+x(f'(0)) first two terms

The Attempt at a Solution


So I have found the Maclaurin expansion of cos(x) to be 1. This seems ridiculous to me so I'm wondering if its correct?
then:
1-2x2=0 so x=+-(sqrt(2)/2)
=+-.239755

I'm not sure what to say about the accuracy??
FYI this is an exam practice Q
Thanks
 
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You want the first two non-vanishing terms. Go to higher order in the expansion.
 
ok, non vanishing means not 0?
 
now I get cos(x)=1-x^2/2
and the solution is +-0.816497
the actual answer is +-.63456 - seems reasonably accurate?
 

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