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11-4 Applications
This program uses the Newton-Raphson method to find the roots (zeros) of a
function numerically.
Find the roots of e
x
ì
3X.
This program uses the Newton-Raphson method to find a root
of
Y1
based on an initial guess. The program prompts for the
initial guess. One way to make this initial guess is to graph
and trace the function, and then enter X as the guess.
PROGRAM:NEWTON
:INPUT "INITIAL X=",X
Input initial guess.
:LBL N
Begin loop.
:X
ì
Y1/NDERIV(Y1,X,X)
→
R
Calculate new root.
:DISP R
:PAUSE
:IF ABS (X
ì
R)
≤
ABS (X/1
í
10)
Test for convergence.
:STOP
:R
→
X
Estimate with new root.
:GOTO N
Follow this procedure to solve the problem.
1. Press
3
and select
FUNC
.
2. Enter the program.
3. Press
(
. Enter the expression
e
õì
3X
to define
Y1
.
4. Graph the function using
ZDECIMAL
from the
ZOOM
menu.
Program: Newton’s Numerical Solve Routine
Problem
Program
Procedure