# AP Calculus BC : Maclaurin Series for exponential and trigonometric functions

## Example Questions

### Example Question #251 : Series In Calculus

Write out the first three terms of the Taylor series about  for the following function:

Explanation:

The Taylor series about x=a for a function is given by

For the first three terms (n=0, 1, 2) we must find the zeroth, first, and second derivative of the function. The zeroth derivative is just the function itself.

The derivatives were found using the following rules:

Now, using the above formula, write out the first three terms:

which simplified becomes

### Example Question #1 : Maclaurin Series For Exponential And Trigonometric Functions

Find the Maclaurin Series of the function

up to the fifth degree.