Use a calculator to solve equations using Newton's Method. (TI-85/86)

General method: Write the equation in the form f(x)=0. Start at a first approximation, x₀, of the solution. Go to the point on the graph of y = f(x) with this number as its x-coordinate. Follow the tangent at that point to its intersection with the x-axis. The x-coordinate of this intersection is x₀-f(x₀)/f '(x₀) which becomes the next (hopefully better) approximate solution. Repeat this process with the new, better, approximation.

Program:
PROGRAM:Newton
:x-y1/y2x
:Disp x,y1

To use this program, place the formula for f(x) as y1 and the formula for f '(x) as y2 in the "y=" menu. Place an initial guess, x₀, for the solution into x. Execute the program. Continuing to press the enter key will display the successive approximations. The second number printed (y1) will be a measure of the success of the process. Another, probably better, measure will be the difference between successive values of x.

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