Consider the function f(x)=x/(ex-1)+x/2.
(a) f has a so-called "removeable singularity" at x=0, where it is (so far) undefined. What value should we assign to f(0) to make f continuous at x=0?
(b) With this taken care of, f actually has a Taylor series about x=0. Find the first 10 terms or so of this Taylor series (use CALCULATOR/MAPLE)
(c) What pattern do you notice in the degrees of the terms in the Taylor polynomials?
(d) Prove the property that you noticed in (c).