### Electronic Proceedings of the Eleventh Annual Conference on Technology in Collegiate Mathematics

CONTRIBUTED PAPER: 11-C36

### Newton Method and HP-48G

De Ting Wu
Departament of Math.
Morehouse College
830 Westview Dr. S.W.
Atlanta, GA. 30314
Phone: (404) 681-2800 Ext.2459
E-mail: dtwu@morehouse.edu

#### ABSTRACT

Newton Method is an often-used procedure to find the approximate values of the solution of an equation. Now, it is covered by most textbooks of Calculus as an application of derivative.

When using Newton Method, usually we follow 3 steps:

• Step 1. Locate the solution and make a good initial guess;
• Step 2. Compute f'(x) and set up the iterative formula;
• Step 3. Perform calculation to find approximations of solution up to the required accuracy.

It should be emphasized the Step 1 is significant and difficult. Since the sequence of approximations may not coverge if the initial guess is selected blindly. And, some -time Step 2 is formidable if f(x) is complicated. Moreover, Step 3 always is a time-consuming job. However, HP-48G can help a lot when using Newton Method.

This approach is as follows:

1. Use "Plot Application" of HP-48G to graph the equation so that it is easy to locate the solution and make good initial guess.
2. Use the program "ITF" to set up the iterative formula. ITF:<< DUP x d/dx / x SWAP - 'NF' STO>>
3. Use the program "APV" to compute the approximate values. APV:<NUM DUP 'X' STO>>

Finally, an example is given to illustrate this approach.

Also, this approach make it easy to grade the problem of Newton Method with different initial quess.