11-02-2019, 12:10 AM

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!

SlideRule

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!

SlideRule