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# Iterations watch

1. Hi,

The iteration x = cosx with x0 = 0.7. How may repetitions are needed to obtain an approximation within 10^-6 of the root.

I have no idea how to tackle this question, any help is much appreciated.
2. (Original post by ChemBoy1)
Hi,

The iteration x = cosx with x0 = 0.7. How may repetitions are needed to obtain an approximation within 10^-6 of the root.

I have no idea how to tackle this question, any help is much appreciated.

Well, what does your module content say about questions like these?

What type of iteration scheme do you use?

Note that this equation as an exact root of and we are approximating it by therefore there is some error. This error is how far away our approximation is from , so we say , and we should have that . In your question, we are interested in the distance from the root, which means that our approximation could be on either side of the exact root thus the error is +ve/-ve but we can just impose the condition that . You wish to find the first value of for which which means that

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