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

21 days ago
140
Science Education Taylor polynomials linear approximation laboratory project stewart calculus mathematics math example quadratic approximation polynomial approximation 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!

Video notes and playlist:

- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh45-at7nZj17TkNC9A
- Excel File: https://1drv.ms/x/s!As32ynv0LoaIh45_mdeGmW3eOH4DKQ
- HIVE notes: https://peakd.com/mathematics/@mes/laboratory-project-taylor-polynomials-question-4-approximating-square-roots
- Laboratory Project playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GMTZJWnswRe2BYAL-Y2CeB

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 .

------------------------------------------------------

Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

MES Links: https://mes.fm/links

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes

Email me: contact@mes.fm

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

Loading 1 comment...