Let f(x) = 1/(1-2x).
a. Find the first five terms in the Taylor series about x = 0 for f(x).
b. Find the interval of convergence for the series in part (a).
c. Use partial fractions and the result from part (a) to find the first five terms in the Taylor series about x = 0 for g(x) = 1/(1-2x)(1-x).
In this solution, a complex function is considered in terms of analyzing the terms in the Taylor series and the interval of convergence. Furthermore, partial fractions are used to find terms belonging to the Taylor series. The solution is detailed and well presented in an attached Word document.