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