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Taylor Series and Polynomials : Removable Singularity, Continuity and Finding Terms

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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).

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Taylor Series and Polynomials, Removable Singularities, Continuity and Finding Terms are investigated. The solution is detailed and well presented.

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(a) Since , then we can assign to ...

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