E1: Select the first predefined function sine. You will see the 3rd approximation. Draw the model point to x = 1 and choose the 1st approximation (twice activating -1). Interpret the result. Does the second zero difference point have any significance for the Taylor approximation?
E2: Increase the order step by step and interpret the results.
E3: One would expect that increasing orders alternate in symmetry. That is not always visible, as characteristic parts of the approximating curve may be outside of the variable ranges. Adjusting parameters will recover the expected regularity.
E4: Return to the default order. Draw the model point to x = 0. Why do first and second order appear identical? (inflection point). Shift the model point slightly and you will see the difference again.
E5: Choose a low order (3 - 4) and draw the model point. Vary b and interpret the result.
E6: Select the power function, default setting will a parabola of second grade. Why do you not see a Taylor approximation of 3rd grade? Why is a difference of zero indicated over the whole range? (for the second grade parabola already the 2nd order Taylor approximation is identical to the function).
E7: Chose m = 5 for the power function and repeat E6.
E8: Experiment with other predefined functions.
E9: Write your own function into the function field. Adjust scales by using the slider parameters or by proper constants in the formula.