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I was told to find the "bounds on the error" in a problem in Spivak's Calculus, but I have no idea what that means.

Use the third degree Taylor polynomial of $\cos$ at $0$ to show that the solutions of $x^2=\cos x$ are approximately $\pm\sqrt{2/3}$, and find bounds on the error.

I recognize that this reduces to simply $1 - x^2/2! + R(x) = x^2$ and that $R(x)$ is the error. So, um, if we don't have the $R(x)$, since it's probably small, we get the needed approximate solution. Am I on the right track? What do I need to do to make this formal?

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    Go back a couple of pages. Spivak gives you an expression for R(x). You can use that and bound it, given it your approximate solution.2012-01-18
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    @SimonS I think I am having a hard time understanding the concept of "bounding" something... but R(x) =< x^4/(4!). I am not sure what I am supposed to do with this though...2012-01-18

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