At the left side of the window one of eight different base functions y = f(x) can be selected by radio buttons. A suitable x range 0 < x < 2a is attributed to each of them.
When opening the simulation, the Gaussian function will be activated and is drawn as a blue curve. The quadratic Taylor approximation around the origin is shown in magenta.
At the top of the window there are 10 radio buttons to select a Taylor approximation (expansion) around a model point xo, of index 0 (constant value y0) to 9 (considering up to the 9th derivative in x0, y0 ). The selected approximations is drawn in the color of the radio buttons .
When check box all is activated all approximations are shown simultaneously. By deactivating option buttons arbitrary combinations can now be selected and compared.
The model point x0, y0 is shown as a red dot. It can be drawn with the mouse to calculate the expansion around an arbitrary model point.
Reset Dot returns the model point to its default position.
The first number field at the left shows the value of the function y0 in the model point x0, y0.
The other number fields show the factors of the power functions ( x-x0 ) n in the Taylor series, as
f5 = y(5)/5!
Very small numbers at high index may indicate numerical artifacts.