High School Math : Understanding Taylor 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