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Calculus and Beyond Homework Help
Estimate number of terms needed for taylor polynomial
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[QUOTE="timnswede, post: 5017113, member: 510024"] [h2]Homework Statement [/h2] For ln(.8) estimate the number of terms needed in a Taylor polynomial to guarantee an accuracy of 10^-10 using the Taylor inequality theorem. [h2]Homework Equations[/h2] |Rn(x)|<[M(|x-a|)^n+1]/(n+1)! for |x-a|<d. [h2]The Attempt at a Solution[/h2] All I've done so far is take a couple derivatives of ln(x): 1/x -1/x^2 2!/x^3 -3!/x^4 and made a general (-1)^(n+1) (n-1)!/(x^n) At this point I am lost, am I supposed to assume a=0? Then M, which is the absolute value of the n+1 derivative would be n!/.8^(n+1). And plugging that into the Taylor inequality equation the .8^(n+1) would cancel and so would the n! and I would be left with 1/n+1<10^-10, which gives me a really big number, even though the answer should be 14. What am I missing? EDIT: It looks like there might be some missing information. My professor sent the solution out, and to me it looks like he is using a=1. Can someone confirm that? [ATTACH=full]176263[/ATTACH] [/QUOTE]
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Estimate number of terms needed for taylor polynomial
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