This applet draws the graph of y = sin(x) along with its Maclaurin polynomial (Taylor polynomial at c=0). The user can specify the degree of the approximating polynomial and then increment it with a push of a button.
Type of Material:
A Java-enabled browser.
Identify Major Learning Goals:
To illustrate the concept of Taylor polynomial approximation.
Target Student Population:
Students in Calculus II
Prerequisite Knowledge or Skills:
College Algebra, Calculus I
Evaluation and Observation
This applet does one thing and one thing only: it draws a graph of a Taylor polynomial approximating y = sin(x) in the neighborhood of the point c = 0. A user can change the degree of the polynomial either by manually typing it or by clicking on the Next button. The latter method increments the degree by two with each click and allows the user to observe the resulting quality of approximation.
The site could use an introductory paragraph explaining Taylor approximation and perhaps giving a formula for a Maclaurin polynomial for y = sin(x) of degree n.
Potential Effectiveness as a Teaching Tool
This applet is a great visual aid for a one-time in-class demonstration in a Calculus course. Traditionally, Taylor approximation is one of the topics that students find hard to absorb. This dynamic applet should help students grasp the concept of Taylor approximation.
The use of the applet is very limited. It would certainly widen the use if one could have a way to change the input function (or at least choose from a list of popular ones) and move the center of approximation.
Ease of Use for Both Students and Faculty
The applet is extremely easy to use since it has only two control buttons and one input box.