#### animating plots of taylor polynomials (28.2.02)

In attempting to show students Taylor polynomials of successive degrees, we tried deﬁning the ﬁrst few
via the loop

This worked.

Next we hoped to plot the polynomials one after the other in the same window, but the animate
command

produces an empty plot.

We’ve found a very elaborate workaround but it seems the basic idea - step from one member of an
indexed list to another - ought to work.

Animate requires s to be a real parameter, not integer. Use instead

or, in Maple 7, the more elegant syntax

While I applaud your eﬀorts to show your students the mechanics of creating
these animations, you may be interested in also showing them my worksheet
"Animation of Taylor series converging to their generating functions" available at the
Maple Applications Center http://www.mapleapps.com.

This produces labelled animations several orders of magnitude faster than your example above, handles
discontinuities, and most of the full range of plot options.

For example

animates the complicated, discontinuous function f and its ﬁrst 50 Taylor polynomials expanded at x=Pi
with view window [0..2*Pi, -10..10] using 1.3 seconds and neglible memory on a Pentium II 400
MHz.

The comments in my code give several pointers on how to produce these high-speed animations.

Animate works best when the animation variable is continuous. It is possible to achieve this for your
situation but it’s not intuitive or simple.

I prefer to create a list of plots and then animate these with the display command. For example,

The animate command is not very versatile. I almost never use it. Instead, create plot structures for
each of your functions:

Then use display with the option insequence=true

You might want to look at ”Animations for the Calculus Classroom” in the Maple Applications Centre
for some further examples.