# High School Math : Taylor and Maclaurin Series

## Example Questions

### Example Question #1 : Understanding Taylor Series

Give the term of the Maclaurin series of the function       Explanation:

The term of the Maclaurin series of a function has coefficient The second derivative of can be found as follows:    The coeficient of in the Maclaurin series is therefore ### Example Question #82 : Calculus Ii — Integrals

Give the term of the Taylor series expansion of the function about .      Explanation:

The term of a Taylor series expansion about is .

We can find by differentiating twice in succession:        so the term is ### Example Question #1 : Understanding Maclaurin Series

Give the term of the Maclaurin series expansion of the function .      Explanation:

This can most easily be answered by recalling that the Maclaurin series for is Multiply by to get:  The term is therefore .

### Example Question #2251 : High School Math

Give the term of the Maclaurin series of the function .      Explanation:

The term of a Maclaurin series expansion has coefficient .

We can find by differentiating three times in succession:     The term we want is therefore ### Example Question #2252 : High School Math

Give the term of the Maclaurin series expansion of the function .      Explanation:

The term of a Maclaurin series expansion has coefficient .

We can find by differentiating twice in succession:       The coefficient we want is ,

so the corresponding term is .

### All High School Math Resources 