# Generating MacLaurin series with a Ti84 Basic program

## Information of the program MacLaurin.8xp

This program calculates the first 6 terms of the MacLaurin series of a function around x=0. MacLaurin series is a special type of Taylor series (series around x=0) and is used in computer science, calculus, physics and higher-level mathematics. It is a series that is used to create an estimate (guess) of what a function looks like. To calculate the terms of the MacLaurin series, a Ti Basic program is written. The program will be demonstrated on the basis of some well-known series. For the MacLaurin series, it yields:

### Example 1 : series of sin(x)

## The program : MacLaurinseries.8xp

#### Example 1: MacLaurin series of sin(x)

sin(x)=x-0.1666x+0.00833x^3. The results show an excellent performance for the Ti-84 and can be used as a check of your analytically derived limit.

### Example 2

Error in the 5th term (f) = (.02740-.02734)*100%/0.2734 =0.22%.

Conclusion: Results of the Ti84 agree very well with the analytical results, but be aware that the Ti84 results are calculated with a numerical program and give only a good approximation of the analytical results. For a copy of the program send a mail to frieboon@gmail.com or do a chat and tell me which Ti84 model you own because then I can send you the right program