GRAPH1, Page 2 - HEWLETT ~ PACKARD

RUN

RUN GRAPH1

PLEASE TYPE THE CODE NUMBER <12121" 22121" 30eJ" 42121" 5321) OF THE FUNCTION THAT YOU ~ANT TO ~ORK ~ITH.

FUNCTION11021

TYPE A VALUE FO~ X.

1-2

X .. -2 Y .. 4 01 ^~-4 02

..

2 TY'PE A VALUE FOR X.

1-1

X ^=: -1 Y a 01

·

^-2 ⁰²^a ²

TYPE A VALUE FOR X.

X .. 21 V ^:0 21 01 ^a 21 02 ^=: 2 TYPE A VALUE FOR X.

X :0 1 Y :0 01

·

² ⁰²

^..

TYPE A VALUE FOR X.

X .. 2 Y • 4 01

·

⁴ ⁰²

^..

IF YOU HAVE ENOUGH INFORMATION ABOUT THIS FUNCTION"

TYPE 1 ; FOR MORE INFORMATION" TY?E 2 '?1

TO OBTAIN ANOTHER FUNCTION TYPE ITS CODE NUMBER (12121; 22121" 32121" 42121" OR 52121). TO STOP THE PROGRAM"

PRESS CTRL/C" THEN PRESS RETURN.

F'UNCTION'?42121

TYPE A VALUE FOR X 1-121

X .. -121 Y .5442122 01 ~ -.8392172 02 II -.5442122 TYPE A VALUE FOR X

1-2.5

x ..

^-2.5 Y • -.598472 01 • -.8211144 02· .598472 TY'PE A VALUE FOR X

121

X .. 21 V .. 3 01

.

^{1 •} ^{02. 21}

TYPE A VALUE FOR X 12.5

X .. 2.5 V .. .598472 01 .. -.8211144 02 .. -.598472 TY'PE A VALUE FOR X

1121

X" 121 y . -.5442122 01. -.8392171 02" .5442122 IF YOU HAVE ENOUGH INFORMATION ABOUT THIS FUNCTION"

TYPE 1; FOR MORE INFORMATION" TY?E 2 11

TO OBTAIN ANOTHER FUNCTION TYPE ITS CODE NUMBER (12121" 221eJ" 32121" 4321" OR 52121). TO STOP THE PROGRAM"

PRESS CTRL/C" THEN PRESS RETURN.

FUNCT ION'?

DONE

TITLE:

DESCRiPtiON:

INSTRUCTIONS:

SPECIAL

CONSIDERATIONS:

ACKNOWLEDGEMENTS:

August 1976

MATHEMATICS (EDUCATION) (801)

CONTRIBUTED PROGRAM

BASIC

COMPUTER-AUGMENTED CALCULUS TOPICS

GRAPH2 36666 This program is designed to provide information to students about functions.

For a selected f(X) and input value of X, the program prints the values of the first and second derivatives of f(X). The student should graph the values and attempt to discover what f(X) is.

The program contains five different functions, on lines 220, 390. 490.

580 and 680. All functions are in the form Y=f(X) .

. The user is asked to select one of the five functions by typing 100. 200.

300, 400. or 500.

Then the program asks for a value for X, and the user has 5 opportunities to input values of X, and obtain the values of the first and second deriv-ative of the unknown f(X). After five values of X have been evaluated.

the program asks for an input of 1 or 2. representing:

1. Enough information has been obtained.

2. Not enough information has been obtained; let me try 5 more values of X.

If option 1 is selected. another function may be selected.

This program is one of 7 which accompany the Project Solo Module "Computer-Augmented Calculus Topics" of the Hewlett Packard Curriculum Series.

To change the functions, retype lines 220, 390, 490, 580, and/or 680.

Functions are in the form LET Y=f(X).

FOR INSTRUCTIONAL PURPOSES

Suitable Courses: Mathematics (Secondary, College); Elem. Computer Science

Stu~ent Background Required: Calculus (can be concurrent); BASIC The curriculum material listed below is available for classroom implemen-tation of this program.

HP 5951-5611 Computer-Augmented Calculus Topics HP 5951-5612 Classroom Set (30 books)

For ordering information of curriculum material, contact:

Hewlett-Packard Computer Curriculum Project Scientific Press

1629 Channing Ave.

Palo Alto, California 94303

Project Solo

University of Pittsburgh

GRAPH2. Page 2

TI'TLE:

DE:SCRIPTION:

INSTRUCTIONS:

SPECIAL

CONSIDERA nONS:

ACKNOWLEDGEMENTS:

August 1976

MATHEMATICS (EDUCATION) (801)

CONTRIBUTED PROGRAM

BASIC

COMPUTER-AUGMENTED CALCULUS TOPICS

INTEGR 36667 This program computes an approximation to the definite integral of a function over a supplied interval on the X-axis. using the trapezoidal method of approximation.

The desired function is supplied as program line 250. in the form 250 LET Y=f( X)

During the run. the user is asked to input A and B. which are the lower and upper bounds of the desired interval on the X-axis.

The program then asks the number of approximating trapezoids (N must be greater than 0).

When the program has printed the resulting approximation. the user is asked to select option 1. 2. or 3 which represent:

1. Change the number of approximating trapezoids.

2. Change A and B.

3. Terminate the program.

This program is one of 7 which accompany the Project Solo Module "Computer-Augmented Calculus Topics" of the Hewlett Packard Curriculum Series.

To change the function. line 250 must be retyped before running the program.

FOR INSTRUCTIONAL PURPOSES

Suitable Courses: Mathematics (Secondary. College): Elem. Computer Science Student Background Required: Calculus (can be concurrent); BASIC

The curriculum material listed below is available for classroom implemen-tation of this program.

HP 5951-5611 Computer-Augmented Calculus Topics HP 5951-5612 Classroom Set (30 books)

For ordering information of curricul~m material, contact:

Hewlett-Packard Computer Curriculum Project Scientific Press

1629 Channing Ave.

Palo Alto, California 94303

Project Solo

University of Pittsburgh

r

NTEGR. PaC)e 2

RUN

250 LET Y.X'2-2.~

RUN INTEGR

THIS PROGRAM COM?UTES APP~OXIMATIONS TO THE DEFINITE INTEGRAL OF THE FUNCTION WHICH YOU SUPPLIED ON LINE 250~ OVER AN INTERVAL (A~B).

NO~ TYPE A VALUE FOR A?l TYPE A VALUE OF B13

HOW MANY SUBINTERVALS DO YOU WANT [A~B) DIVIDED INT0716 THE INTERVAL IS (1 ~ 3 ].

THE NUMBER OF APPROXIMATING TRAPEZOIDS IS 16 THE APPROXIMATION IS ' ••••••• 671875

••••••

TY?E THE CHANGE CODE?l

HOW MANY SUBINTERVALS DO YOU WANT [A~B] DIVIDED INT01256 THE INTERVAL IS [ 1 ~ 3 ].

THE NUMBER OF APPROXIMATING TRAPEZOIDS IS 256 THE APPROXIMATION IS ••••••• 666687

TYPE THE CHANGE CODE?2 NOW TYPE A VALUE rOR A?-2 TYPE A VALUE OF B?2

••••••

HOW MANY SUBINTE~VALS DO YOU ~ANT CA~B] DIVIDED INT0732 THE INTERVAL IS [-2 ~ 2 l.

THE NUMBER OF APPROXIMATING TRAPEZOIDS IS 32 THE APpqOXIMATION IS •••••• 5.34375

••••••

i~E iHE CHANGE CODE?l

HOW MANY SUBINTERVALS 00 YOU VANT [A~BJ DIVIDED INT0764 THE INTEqVAL IS (-2 ^~ 2 ].

THE NUMBER OF APPROXIMATING i~APEZOIDS IS 64 THE APPROXIMATION IS •••••• 5.33594

••••••

TYPE THE CHANGE CODE?3 DONE

August 1976

TITLE:

DESCBIPTlON:

INSTRUCTIONS:

ACKNOWLEDGEMENTS:

MATHEMATICS (EDUCATION) (801)

CONTRIBUTED PROGRAM

BASIC

LIMIT OF (SIN X)/X

sin x

LIMSIN

36622

This program demonstrates that the limit of x ,as x approaches 0, equals 1, provided x is measured in radians. If x is measured in degrees, the limit equals approximately .017.

OBJECTIVES:

sin x

A. To demonstrate the manner by which the limit of x is approached.

B. To show that degree measure does not yield the same solution as radian measure.

PRELIMINARY PREPARATION:

A. Student - Knowledge of degree vs. radian measure B. Materials - None

DISCUSSION:

Following the computer type-out. the teacher will use the analytic method to evaluate the limit. Prior to this discussion, the student should be reminded of the area formulas for a triangle and for a sector in terms of the central angle measured in radians. A geometric diagram should be presented showing the sector lying between two

tri-angles.

o

Bara. irZ .in

ell iz2e

~ ^ir2tan

e

Circular Sector with Circum8cribed ^andIaacrlbed triaDlle.

Dans le document HEWLETT ~ PACKARD (Page 66-71)