Representing a function as a Power Series. Suppose that we want to represent the function f(x) = ln(2x + 7) as a power series centered at zero. We can start by finding the power series representation (centered at zero) for the derivative of the function, f'(x). The power series representation (centered at zero) for f'(x) is: f'(x) = Σ 71-0 The series you found above converges on the interval Next, integrate term by term the series you found. This will enable you to write the series representation for f(x) = ln(2x + 7). In (2x + 7) + n=0 Note: the second to last blank above is for the constant of integration can which be found by substituting x = 0 into both sides of the equation containing the antidifferentiated series.

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