Approximating Functions with Polynomials

Complex functions can often be approximated over a region of their domain by a polynomial. [br][br]This environment lets you explore this phenomenon for three types of function.[br][br]Move the black dot on the x axis to the region of the domain where you would like the approximation to be good. Slider the slider the choose the order of the approximating polynomial.[br][br]If you place the black dot on the origin[br]- where is the polynomial approximation best for the exponential function?[br]- why do the approximating polynomials for sin(x) contain no even powers of x?[br][br]Why does this seem to break down for the absolute value function?[br][br][i][b]If you are using a laptop or desktop computer please[br]run this as a Java applet - see option below window[br]- be patient - it may take a while to load the Java version[br]- if you see an "unresponsive script" message - choose "continue"[/b][/i]

Information: Approximating Functions with Polynomials