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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: 

Formula Maclaurin series

Example 1 : series of sin(x)

Maclaurin series of sin(x)

The program : MacLaurinseries.8xp

Example 1: MacLaurin series of sin(x)

Starting Calculating MacLaurin series Ti84-plus program
Calculating MacLaurin series with a Ti84-plus program 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

series for V(l1+x)
Calculating MacLaurin series with Ti-Basic program of V(1+x)

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

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