Mathematics HL IA (Grade: 7)

I. Introduction

My interest in Taylor series arose when I became curious of how our graphic display calculators actually calculate a value when we plug-in an value into a function. As a calculator would not be able to have every single value for any function, there must be an algorithm that the calculator uses to calculate functional values. I searched up what kind of calculations our graphic calculators are actually doing, and what I have found was the marvelous series – Taylor series.

A Taylor series is “a series expansion of a function about a point” (Abramowitz). What our calculators do to calculate a functional value is that, they approximate a function into this Taylor series give approximate values when we input a value. I became curious of the explicit process ‘how’ this Taylor series is actually used and how reliable it is to use to calculate any functional value on the calculator. Therefore I developed my aims of this exploration: 1) Investigate in how Taylor series is used in graphic display calculators through its proof and applications and 2) investigate in the approximation error produced by Taylor series.