14.3 Taylor polynomials (1) - The definition with the limit
Taylor polynomials are good approximations for a function near a point. We can define them via three different properties: 1. The one with the limit (this video): https://youtu.be/aCFR5CABSA0 2. The one with the derivatives: https://youtu.be/sNWY1w8YocM 3. The explicit formula: https://youtu.be/c-rI1zMj0wA Other related videos: * Playlist on power series and Taylor series: https://www.youtube.com/playlist?list=PLlwePzQY_wW9h32ZwS6CYsY4eR_b2pE9j * Examples: The main four Maclaurin series (and polynomials): https://youtu.be/o-RSENE_Yus 0:00 Introduction 0:27 Goal 1:07 What is a "good" approximation? 1:50 Finding conditions for "small" remainder 2:40 What does "FAST" mean? 4:01 Definition of approximation 5:20 Shifting the scale 5:54 Definition of approximation for any a 6:24 Taylor polynomials: first definition 7:37 Debrief
Taylor polynomials are good approximations for a function near a point. We can define them via three different properties: 1. The one with the limit (this video): https://youtu.be/aCFR5CABSA0 2. The one with the derivatives: https://youtu.be/sNWY1w8YocM 3. The explicit formula: https://youtu.be/c-rI1zMj0wA Other related videos: * Playlist on power series and Taylor series: https://www.youtube.com/playlist?list=PLlwePzQY_wW9h32ZwS6CYsY4eR_b2pE9j * Examples: The main four Maclaurin series (and polynomials): https://youtu.be/o-RSENE_Yus 0:00 Introduction 0:27 Goal 1:07 What is a "good" approximation? 1:50 Finding conditions for "small" remainder 2:40 What does "FAST" mean? 4:01 Definition of approximation 5:20 Shifting the scale 5:54 Definition of approximation for any a 6:24 Taylor polynomials: first definition 7:37 Debrief