Chapter 10, Problem 60RE

Let f(x)=e(x-1)^2-1/(x-1)2  for x ≠ 1 and f(1)=1 a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1 b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1 c. Determine the interval of convergence for the series given in (b). d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.

Find the first 3 terms of the Taylor series for f(x) = ln(x) centered at 4.

Find the first four terms of the Taylor series for xcos(2x).