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Notes on Taylor and Maclaurin Series
A Maclaurin series is a power series - a polynomial with carefully selected coefficients and an infinite number of terms - used to approximate arbitrary functions with some conditions (e.g. differentiability).
This approximation will be decent very close to 0 (at least in the direction of the slope), but will become progressively worse as we get farther away from 0. The light blue lines are successive approximations, with k terms of the power series included: This section shows how one arrives at the formula for the Maclaurin series, and connects it to the intuition of equating derivatives.
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