Laboratory Project: Taylor Polynomials: Question 4: Approximating Square Roots


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    Published on Dec 02, 2020
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    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:!As32ynv0LoaIh45-at7nZj17TkNC9A
    Excel File:!As32ynv0LoaIh45_mdeGmW3eOH4DKQ?e=mqzYud

    View video notes on the Hive blockchain:

    Related Videos:

    Laboratory Project: Taylor Polynomials: Question 3: (x - a) Approximation Form:
    Laboratory Project: Taylor Polynomials: Question 2: Approximation Accuracy:
    Laboratory Project: Taylor Polynomials: Question 1: Quadratic Approximation:
    Taylor Polynomials - Introduction and Derivation:
    Linear Approximation - Introduction and Examples:
    Differentials Notation in Linear Approximation:
    Newton's Method of Linear Approximation - Introduction: .


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