David Little  
Mathematics Department Penn State University Eberly College of Science University Park, PA 16802 
Office: 403 McAllister Phone: (814) 8653329 Fax: (814) 8653735 email:dlittle@psu.edu 



Taylor Polynomials
The following applet can be used to graph the Taylor polynomial of degree n, T_{n}(x), and/or the remainder function, R_{n}(x), for the given function y=f(x), centered at x=a. Simply enter the function f(x) and the values a and 0 ≤ n ≤ 50. The applet can also be used to approximate the value of f(b) with T_{n}(b), for b near a. The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change this value by using the up/down arrow keys, clicking on the graph of y=f(x) or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the xaxis in radians (i.e. multiples of pi), click on the graph and press "controlr". To switch back, simply press "controlr" again. Here is a list of functions that can be used with this applet. Warning: The below applet does very well graphing Taylor polynomials of large degree (e.g. n=50) for exponential and trigonometric functions. However, the degree of Taylor polynomials of other functions or compositions and/or quotients of functions should be limited to 5 (i.e. n ≤ 5) © 2005 David P. Little Download this applet for offline viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems 