Taylor Series and Taylor/Maclaurin Series Investigation

Mathematical Methods

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25 Pages • Essays / Projects • Year Uploaded: 2023

Calculators and computers struggle with complex functions. So how can your calculator find the value of things like sin (𝜋/4)? It can’t store all possible answers in its memory. Instead, computers use polynomials to approximate complex functions, such as sin(𝑥). Overview In this investigation you will call upon your understanding of differential calculus, algebra and limits to approximate values of known functions using Taylor polynomials. You will also examine the accuracy of these polynomials and develop an understanding of the necessary limitations of the Taylor or Maclaurin series. Your final investigation will be a maximum of 15 pages, have a minimum font size of 10 and use the Calibri, Times New Roman or Arial fonts. It should include: • An introduction detailing what the investigation will entail. • A main body looking at the working and explanations. • A conclusion giving a detailed summary of all results. You are not to use any information from the internet, particularly ChatGPT, to write all or part of your investigation. It must be your own work, not written by another person or AI.

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