Laboratory Project: Taylor Polynomials: Question 3: (x - a) Approximation Form скачать в хорошем качестве

Laboratory Project: Taylor Polynomials: Question 3: (x - a) Approximation Form

In this video I go over Question 3 of the Laboratory Project: Taylor Polynomials, and this time revisit the quadratic approximation but instead use a slightly different notation. In Question 1 I illustrated how the quadratic or parabola or 2nd order polynomial approximation P(x) = A + Bx + Cx^2 can be used to approximate a function f(x) at x = a, with the conditions that P(a) = f’(a), P’(a) = f’(a), and P’’(a) = f’’(a). But in this video I show that it is often preferable to use a slightly different notation and instead use P(x) = A + B(x – a) + C(x – a)^2. The only difference in using this form is that the constants A, B, C will not necessarily be the same. This notation has the benefit in that determine the constants with the 3 conditions listed above is fairly easy because when we input x = a into P(x) or its derivative, most terms vanish because a – a = 0. When we solve for the constants, I show that we obtain the function P(x) = f(a) + f’(a)(x – a) + f’’(a)(x – a)^2, which is a very convenient form to determine the constants, just from f(x) and its derivatives at x = a. Furthermore, this is the basis for Taylor Polynomials which I will be illustrating in further parts of this Laboratory Project, so make sure to watch this video and fully understand this concept! --- UPDATE: Error at the end which I wrote f"(a)(x-a) instead the correct term of f'(a)(x-a). --- Video notes and playlist: PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh45zx... HIVE notes: https://peakd.com/mathematics/@mes/la... Laboratory Project playlist:    • Laboratory Project: Taylor Polynomials   Related Videos: Laboratory Project: Taylor Polynomials: Question 2: Approximation Accuracy:    • Laboratory Project: Taylor Polynomials: Qu...   Laboratory Project: Taylor Polynomials: Question 1: Quadratic Approximation:    • Laboratory Project: Taylor Polynomials: Qu...   Taylor Polynomials - Introduction and Derivation:    • Taylor Polynomials - Introduction and Deri...   Linear Approximation - Introduction and Examples:    • Linear Approximation - Introduction and Ex...   tan(x) = sin(x) = x and cos(x) = 1 near x = 0: Linear Approximation in Physics:    • tan(x) = sin(x) = x and cos(x) = 1 near x ...   Differentials Notation in Linear Approximation:    • Differentials Notation in Linear Approxima...   Newton's Method of Linear Approximation - Introduction:    • Newton's Method of Linear Approximation - ...   . ------------------------------------------------------ Become a MES Super Fan!    / @mes   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