Laboratory Project: Taylor Polynomials: Question 4: Approximating S...

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_zoW1mCiELswmsw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/laboratory-project-taylor-polynomials-question-4-approximating-square-roots