1. The problem statement, all variables and given/known data 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. Relevant 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?