Taylor and Maclaurin series are infinite sums based on a parent function that can be used to approximate functions. A Taylor series uses derivatives evaluated at a specific point a, while a Maclaurin series sets a to 0. To find a Maclaurin series, one takes the derivatives of the function and uses them to determine the coefficients in the general term formula with a=0. Examples show finding the Maclaurin series involves taking derivatives, looking for patterns, and plugging a=0 and the coefficients into the general term formula.

1. Taylor/ Maclaurin Series

4. Try a Maclaurin Series with Step 1: find the derivatives for: Remember that this particular function is easy because the pattern is easy to spot.

5. Step 2, use a=0 and find your coefficient (it’s a maclaurin series)

7. The Maclaurin series to MEMORIZE