Laboratory Project: Taylor Polynomials: Question 4: Approximating Square Roots
In this video I go over Question 4 of the Laboratory Project: Taylor Polynomials and this time go over an example on approximating a square root function using the quadratic approximation notation from Question 3. The function I approximate is (x + 3)1/2 which is also the same function I approximated using linear approximation several years ago. Using the notation from Question 1, using (x – a) and at values near a = 1, I show that the quadratic approximation is better than the linear approximation, again as expected. I graph the function as well as the linear and quadratic approximations, as well as develop a spreadsheet to show that near or far from x = a = 1, the quadratic approximation is more accurate than the linear. This is a very good example to get a firm grip on the quadratic approximation method, which as I will show in later parts of this project, is the basis of higher order approximations known as Taylor Polynomials; so make sure to watch this video!
Download the notes in my video:
PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIh45-at7nZj17TkNC9A
Excel File: https://1drv.ms/x/s!As32ynv0LoaIh45_mdeGmW3eOH4DKQ?e=mqzYud
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/laboratory-project-taylor-polynomials-question-4-approximating-square-roots
Related Videos:
Laboratory Project: Taylor Polynomials: Question 3: (x - a) Approximation Form: https://youtu.be/V_u_SHVbTdc
Laboratory Project: Taylor Polynomials: Question 2: Approximation Accuracy: https://youtu.be/MRSs0Qofd_M
Laboratory Project: Taylor Polynomials: Question 1: Quadratic Approximation: https://youtu.be/8bpF3vccvEU
Taylor Polynomials - Introduction and Derivation: http://youtu.be/p2EkXwkbflk
Linear Approximation - Introduction and Examples: http://youtu.be/bXEK8bkWTtM
Differentials Notation in Linear Approximation: http://youtu.be/s0adatWiZg4
Newton's Method of Linear Approximation - Introduction: http://youtu.be/aT4b_5l50RI .
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