Jan 20, 2006
- 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:
- Simulation<br />
- Recommended Uses:
- In-class demonstration
- Technical Requirements:
- 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
- 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
- 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.
- 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.
- The applet is extremely easy to use since it has only two control buttons and
one input box.
- Creative Commons: