In this section we will discuss how to find the Taylor/Maclaurin Series for a function. This will work for a much wider variety of function than the method discussed in the

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The Maclaurin series of a function f ( x) up to order n may be found using Series [ f, x, 0, n] . It is a special case of Taylor series when x = 0. The Maclaurin series is given by f ( x) = f ( x 0) + f ′ ( x

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Example 1: Find the Maclaurin series expansion of the function f (x) = e x. Solution: We will find the derivatives of the given function f (x) = e x. f ' (x) = e x f '' (x) = e x f ''' (x) = e x We can clearly see that f (0) = f ' (0) = f '' (0) = f ''' (0) = . = e 0 = 1. Using the Maclurin series formula, f (x) = f (0)+f (0)x + f (0) 2! x2 + f

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A Maclaurin series is the specific instance of the Taylor series when a=0. Remember that we can choose any value of “a” in order to find a Taylor polynomial. Maclaurin series eliminate that choice and force us to choose a=0.