1 Errors bound for Taylor polynomials 1. (a). Find the 2nd-order Taylor polynomial for f (x) = In(x) centered at a = 1. (b) Use this polynomial to estimate In (1.5). (c) Find an upper bound of the error in your above estimate. (d) Now use this polynomial to estimate In (0.5). (e) Find an upper bound of the error in your above estimate. (f) Let's say now that you need to estimate In(x) for all x between 0.5 and 1.5. Find an upper bound that works for every single one of the x's in the integral [0.5, 1.5]