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**1. Homework Statement**

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.

**2. Homework Equations**

|Rn(x)|<[M(|x-a|)^n+1]/(n+1)! for |x-a|<d.

**3. The Attempt at a Solution**

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 in to 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?

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