Since x - 1 can be calculated precisely, we need to approximate on up to 0.015. We have where is a partial sum of the Taylor series that goes up to (here ) and . Then , and we need to ensure that , i.e., .
The Lagrange form of the remainder is where is some point between and . Since for all n and x, we have . According to my calculations, the least n such that is 5. However, since , it is enough to approximate by , which has only three terms.
I did this check: .