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Maclaurin Series
Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specified function. Let us start out with a few notation and definitions that we'll require.
To find out a condition that must be true in order for a Taylor series to exist for a function let's first describe the nth degree Taylor polynomial of f (x) as,
.
Note: This actually is a polynomial of degree at most n! If we were to write out the sum with no the summation notation this would obviously be an nth degree polynomial.
Derivatives of Trig Functions In this section we will see derivatives of functions other than polynomials or roots of polynomials. We'll begin this process off through taking
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