(38G) Newton's Method

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An excerpt from Appendix E: Graphing Utility Programs, Applied Calculus 6e (Larson);

Programs for graphing calculators are referenced in several sections in the text. This appendix contains translations of these programs for the TI-82, TI-83, TI-85, TI-86, TI-89, TI-92, Casio CFX-9850G, HP 38G, and Sharp EL 9200/9300, arranged by calculator model. Similar programs can be written for other brands and models of graphing calculators.
Enter a program in your calculator, then refer to the text discussion and apply the program as appropriate.

Newton's Method

This program uses Newton's Method to approximate the zeros of a function. Enter both programs into the calculator. Store the expression ƒ(x) in the F1 function in the Function aplet. Be sure F1 is checked. Then graph the function to estimate one of its zeros. The program will prompt you for this estimate.

NEWTON PROGRAM
INPUT X;“ENTER APPROXIMATION”; “ENTER X”;“ ”; 1:
1►N:
X-F(1)X/∂X(F1(X)))►R:
WHILE ABS(X-R)>1E-10
REPEAT RUN “NEWTONLOOP”
END:
ERASE:
DISP 2; “ROOT=”:
DISP 3; R:
DISP 5; “ITER=”:
DISP 6; R:
FREEZE:

NEWTONLOOP PROGRAM
R►X:
X-F(1)X/∂X(F1(X)))►R:
N+1►N

BEST!
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