This program allows the user to investigate Taylor Polynomials either by using common
series for sine, cosine, arctangent, base-e exponential or natural logarithmic functions.
Using this method, you can see the program build the approximating polynomial while you move
the slider. The default setting for the maximum number of terms in the polynomial is 20, but
you can set that higher. Computers can only calculate to about 68! so keep in mind that there
are limitations to how high you can set that maximum.

There is also a 'free input' mode where you can enter a function you like and any center point
and the approximating polynomials will be created on the fly. Keep in mind, that whatever you
set the maximum value for N is really important. The computer must calculate that many derivatives
before the program runs, so functions like sin(x), cos(x), log(x), e^x, and any polynomial are fine
for a setting of 20 or more derivatives because the derivatives are not intensive to calculate.

However, if you enter functions like atan(x), or sec(x) or any other functions where the derivatives
become increasingly more complex, you need to set maximum value of N down to a small number or else
the program will effectively crash while trying to perform that operation.

The recommended values of N for some functions are given below:

$\\atan x$ : N = 6

$\\tan x$ : N = 12

$\\sec x$ : N = 10

In 'Free Input' mode, you can enter any value you want for the center point of the calculation. You
can also enter a calculation because this input gets evaluated before being used. So for instance,
you can enter pi/2, cos(pi) or ln(2) as your center point and the program will evaluate these for you.

You can toggle fullscreen mode with the 'Full Screen' button, which is recommended, and the graphing
window can be resized. The graph can be panned using a finger swipe, or holding shift while clicking
the mouse and dragging. You can zoom in using the mouse wheel, or by pinching with two fingers.


Make sure to click the 'Update' button after choosing a new function or changing the value of
N, as the program does not change automatically with new input.