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Suppose we have a computer program that estimates the root of an equation $f(x) = 0 $ by bisection.

Given that its truncation error $\leq$ a & rounding error for evaluating $f(x)$ is $\leq$ b (for a given range of x), what is the estimated accuracy of the root?

I am told that the Taylor expansion of $f(x)$ would be useful but I don't know how to proceed.

Thanks for any help!

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Hint: At the point $x$ where you think $f(x)=0,$ you only really know that $|f(x)| \lt a+b.$ Then how far off from the real root can you be? You might think about the cases $f(x)=x$ and $f(x)=x^4$, which have rather different behavior.

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    @Ross Millikan: Thanks, Ross. :)2011-08-09