Two questions from this: If the goal of the taylor series is to approximate a function at a point, why is it necessary to find quadratic and higher order approximations if the linear approximation (tangent line) gives you the function's value at the point? Also, why is it by taking the second derivative you get a quadratic approximation?
![Multivariable Calculus 17 | Taylor's Theorem - Examples [dark version]](http://i.ytimg.com/vi/0gADi9YZG_A/mqdefault.jpg)
![Multivariable Calculus 17 | Taylor's Theorem - Examples [dark version]](/img/tr.png)
Two questions from this: If the goal of the taylor series is to approximate a function at a point, why is it necessary to find quadratic and higher order approximations if the linear approximation (tangent line) gives you the function's value at the point? Also, why is it by taking the second derivative you get a quadratic approximation?
You want to approximate around the point, not only at the point.
Yeah, good presentation.
Glad you think so!
Good stuff!
Theres no restriction over the norm of the limit yes? I mean, it can be any norm?
Essentially yes, but we usually take the standard norm.
How are you writing it? What software is it you are taking notes on? Great video!
All these questions are answered on my website, see description :)