CFX-9850G Midpoint, Simpson, Newton methods

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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, HP38G, 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.

Midpoint Rule

This program uses the Midpoint Rule to approximate the definite integral a∫b ƒ(x) dx. You must store the expression ƒ(x) as f1 before executing the program. The program itself will prompt you for the limits a and b and for the number of subintervals η.

======MIDPOINT======
“LOWER LIMIT”?→ A↲
“UPPER LIMIT”?→ B↲
“N DIVISIONS”?→ N↲
0→S↲
(B-A)÷N→W↲
1→J↲
Lbl 1↲
A+(J-1)W→L↲
A+JW→R↲
(L+R)÷2→X↲
S+Wf1→S↲
J+1→J↲
J≤N⇒Goto 1↲
“APPROXIMATION”↲
S


Simpson's Rule

This program uses Simpson's Rule to approximate the definite integral a∫b ƒ(x) dx. You must store the expression ƒ(x) as f1 before executing the program. The program itself will prompt you for the limits a and b and for half the number of subintervals you want to use.

======SIMPSON PROGRAM======
“LOWER LIMIT”?→A↲
“UPPER LIMIT”?→B↲
“N÷2 DIVISIONS”?→ D↲
0→S↲
(B-A)÷(2D)→W↲
1→J↲
Lbl 1↲
A+2(J-1)W→L↲
A+2JW→R↲
(L+R)÷2→M↲
L→X↲
f1→L↲
M→X↲
f1→M↲
R→X↲
f1→R↲
W(L+4M+R)÷3+S→S↲
J+1→J↲
J≤D⇒Goto→1↲
“APPROXIMATION”↲
S


Newton's Method

This program uses Newton's Method to approximate the zeros of a function. You must store the expression ƒ(x) as f1 before executing the program. Then graph the function to estimate one of its zeros. The program will prompt you for this estimate.

======NEWTON PROGRAM======
“ENTER APPROXIMATION”?→X↲
1→N↲
X-f1÷d/dx(f1,X)→R↲
Lbl 1↲
R→X↲
X-f1÷d/dx(f1,X)→R↲
N+1→N↲
Abs (X-R)≥1E-10⇒Goto 1↲
“ROOT=”↲
R◢
“ITER=”↲
N

BEST!
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