Convergence tests for series appear on both sections of the BC Calculus exam. In the multiple-choice section, students may be asked to say if a sequence or series converges or which of several series converge. The Ratio test is used most often to determine the radius of convergence and the other tests to determine the…
One of the great things – at least I like it – about Taylor series is that they are unique. There is only one Taylor series for any function centered at a given point, What that means is that any way you get it, it’s right. Faced with writing the power series for, say, ,…
The seventh in the Graphing Calculator / Technology series Here are some hints for graphing Taylor polynomials using technology. (The illustrations are made using a TI-8x calculator. The ideas are the same on other graphing calculators; the syntax may be slightly different.) Each successive term of a Taylor polynomial consists of all the previous terms…
As I hope you’ve noticed there is a new pull-down on the navigation bar called “Website.” For some years I’ve had a website at linmcmullin.net that lately I’ve been neglecting. I decided to close it in the next few days, and therefore, I move most of the material that is there to this new tab. The…
Recently, there was an interesting discussion on the AP Calculus Community discussion boards about the Lagrange error bound. You may link to it by clicking here. The replies by James L. Hartman and Daniel J. Teague were particularly enlightening and included files that you may download with the proof of Taylor’s Theorem (Hartman) and its…
AP Type Question 10 Sequences and Series – for BC only Convergence tests for series appear on both sections of the BC Calculus exam. In the multiple-choice section students may be asked to say if a sequence or series converges or which of several series converge. The Ratio test is used most often to determine…
How Good is Your Approximation? Whenever you approximate something you should be concerned about how good your approximation is. The error, E, of any approximation is defined to be the absolute value of the difference between the actual value and the approximation. If Tn(x) is the Taylor/Maclaurin approximation of degree n for a function f(x)…
