The Maclaurin series is used to provide a polynomial approximation to complicated functions. Move the slider to change the number of terms in the series (1=constant, 2=linear, 3=quadratic and so on). The blue line shows the mathematical function to be approximated; the red line shows the Maclaurin series approximation and the black line shows the difference between the original function and the approximation. Type your own functions into the input box to see how well the Maclaurin series approximates them with a given number of terms.
See how in general, if you increase the number of terms that the approximation becomes more applicable over a wider range of x. Can you explain why increasing the number of terms from 2 to 3, or from 4 to 5, for sin(x), produces no improvement? Is this also true if you approximate exp(x) ?