Consider the function f(x) = 1 x-2 (a) Compute some derivatives at x = 3 and come up with a formula for the nth derivative f(n) (3). (b) Write out the full Taylor series for f(x) centered at x = 3 in sigma notation. (c) Now write out P,(x), the third degree Taylor polynomial for f(x), centered at x = 3. (d) Use Taylor's Remainder Theorem to estimate how close P,(3.1) is to f(3.1).