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

2. Taylor series A Taylor series is an infinite sum that is based on a parent function. To create a Taylor series from any equation- use to general term: In the general term, a is any value on the function that you use to calculate the derivatives, in Maclaurin series, a=0.

3. Examples Remember the general term Discover patterns in derivatives that will make the solution easier.

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)

6. Now create your Maclaurin series Remember a=0

7. The Maclaurin series to MEMORIZE