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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.
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Trapezoid Rule - Approximating Definite Integrals For this rule we will do similar set up as for the Midpoint Rule. We will break up the interval [a, b] into n subintervals of
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Find the full fourier Series of e^x on (-l,l)in its real and complex forms. (hint:it is convenient to find the complex form first)
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