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Casio CFX-9800G-w Owners Manual - Page 58

d/d71, 3,gX-1'5

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3 Chapter Differential, Integration, and E Calculations II 3.1 How the Unit Calculates Differentials The following is the input format for differentials: EM Elf(x)MalAxID Increase/decrease of x Point for which you want to determine the derivative tildx(f(x), a, Ax) f(a) The differentiation for this type of calculation is defined as: f(a)=Iim f(a+ Ax)-f(a) Ax-t0 Ax In this definition, infinitesimal is replaced by a sufficiently small Ax, with the value in the neighborhood of f (a) calculated as: f(a + Ax)- f(a) (a)= Ax In order to provide the best precision possible, this unit employs central difference to perform differential calculations. The following illustrates central difference. AY Ax f(a + Ax)-f(a- Ax) 2Ax y=f(x) Vy vx a- Ax a a+Ax The slopes of point a and point a+ Ax, and of point a and point a - Ax in function y=f(x) are as follows: f(a + Ax)- f(a) _ Ay f(a)-f(a- Ax) _ Vy Ax Ax Ax Vx - 80 - In the above, Ay/Ax is called the forward difference, while. Vy/Vx is the backward difference. To calculate derivatives, the unit takes the average between the value of Ay/Axand Vyl,Vx, thereby providinghigher precision for derivatives. This average, which is called the central difference, is expressed as: no _1 (f(a+ ox)-f(a) f(a)-f(a- Ax)) Ax _f(a+ Ax)-f(a- Ax) 2A.Y •To Perform a Differential Calculation Example To determine the derivative at point x=3 for the function y= x3 + 4x2 + x-6, when the increase/decrease of xis: defined as dx= s -5. Input the function f(x). 123 uzenEEMEMEI r dX XA3+4X 2+X- 1 Input point x= a for whiCh you want to determine the derivative. Nclx

Section	Page
Contents	19
Handling Precautions	23
Aobut This Manual	23
Chapter1 Getting Acquainted	24
1-1 Keys and Their Functions	25
The Keyboard	25
Key Operations	25
1-2 Modes	28
Set Up Displays	28
Set Up Display Function Key Menus	29
About Display Colors	31
About Function Key lcons	31
1-3 Basic Set Up	32
Default unit of Angular Measurement	32
About the DISP Menu	32
Color Contrast Adjustment	33
1-4 Basic Operation	34
Using the Clear Menu	34
Inputting Calculations	34
Editing Calculations	34
Answer Function	35
Using Multistatements	35
Multiplication Operations without a Multiplication Sign	36
Performing Continuous Calculations	36
Using the Replay Function	36
Built-in Scientific Functions	37
Value Memories	38
Increasing the Number of Value Memories	39
About Memory Names	39
1-5 Using the Function Memory	39
Variable Data (VAR) Menu	40
1-6 Using the BASE Mode	44
1-7 Graphic and Text Displays	46
1-8 Technical Information	46
Calculation Priority Sequence	46
Stacks	47
Value Input and Output Limitations	47
Input Capacity	47
Overflow and Errors	47
Exponential Display	48
Calculation Execution Display	48
When Errors Keep Occurring	48
Chapter 2 Manual Calculations	49
2-1 Arithmetic Calculations	50
Calculations Using Parentheses	50
2-2 Units of Angular Measurement	51
2-3 Trigonometric and Inverse Trigonometric Functions	51
2-4 Logarithmic and Exponential Functions	51
2-5 Hyperbolic and Inverse Hyperbolic Functions	52
2-6 Other Functions	52
2-7 Coordinate Conversion	53
2-8 Permutation and Combination	53
2-9 Fractions	54
2-1O Engineering Symbol Calculations	54
2-11 Number of Decimal Places, Number of Significant Digits, Display Format	55
2-12 Calculations Using Memory	55
2-13 BASE Mode Calculations	56
Conversions	56
Negative Values	56
Arithmetic Operations	56
Logical Operations	56
Chapter 3 Differential, Integration, and Calculations	57
3-1 How the Unit Calculates Differentials	58
To Perform a Differential Calculation	58
Applications of Differential Calculations	59
3-2 How the Unit Calculates Integrations	59
To Perform an Integration Calculation	60
Application of Integration Calculation	60
3-3 ~Calculations	61
Example ~ calculation	61
~ Calculation Applications	62
~ Calculation Precautions	62
Chapter 4 Complex Numbers	62
4-1 Before Beginning a Complex Number Calculation	63
4-2 Performing Complex Number Calculations	63
Arithmetic Operations	63
Reciprocals, Square Roots, and Squares	63
Absolute Value and Argument	63
Conjugate Complex Numbers	64
Extraction of Real and Imaginary Number Parts	64
4-3 Complex Number Calculation Precautions	64
Chapter 5 statistical Calculations	65
5-1 Single-Variable Stetistical Calculations	66
To Enter the Standard Deviation Mode without Data Storage	66
To Enter the Standard Deviation Mode with Data Storage	67
Performing Single-Variable Calculations	68
5-2 Paired-Variable Statistical Calculations	69
To Enter the Regression Mode without Data Storage	69
Linear Regression	70
Logarithmic Regression	70
Exponential Regression	70
Power Regression	71
To Enter the Regression Mode with Data Storage	71
Performing Paired-Variable Calculations	72
5-3 Examples of Statistical Calculations	72
Linear Regression	74
Logarithmic Regression	74
Exponential Regression	75
Power Regression	75
Chapter 6 Using the Matrix Mode	76
6-1 Before Performing Matrix Calculations	77
Entering the Matrix Mode	77
Matrix List	77
Matrix Input	77
Deleting Matrices	79
6-2 Modifying a Matrix	79
Before Modifying a Matrix	79
Row Operations	80
Modifying the Contents of a Matrix	81
Deleting, Inserting and Adding Rows	81
Deleting, Inserting and Adding Columns	83
6-3 Matrix Calculations	84
Arithmetic Operations	84
Calculating a Scalar Product	85
Determinants	86
Transposing a Matrix	86
Inverting a Matrix	87
Squaring a Matrix	87
6-4 Matrix Operation Precautions	88
Chapter7 Equation Calculations	88
7-1 Before Beginning and Equation Calculation	89
Entering an Equation Calculation Mode	89
Clearing the Equation Memories	89
7-2 Linear Equations with Two to Six Unknowns	89
Entering the Linear Equation Mode for Two to Six Unknowns	89
Solving a Linear Equation with Three Unknowns	90
Changing Coefficients	90
Clearing All the Coefficients	91
7-3 Quadratic and Cubic Equations	91
Entering the Quadratic/Cubic Equation Mode	91
Solving a Quadratic or Cubic Equation	91
Quadratic Equations that Produce Multiple Root (1 or 2) Solutions or Imaginary Number Solutions	92
Changing Coefficients	92
Clearing All the Coefficients	92
7-4 What to Do When an Error Occurs	92
Chapter 8 Graphing	93
8-1 About the Graphing Function	94
Specifying the Range of a Graph	94
Initializing the Range Parameter Display Settings	96
8-2 Rectangular Coordinate Graphs	96
Graphing Built-in Scientific Functions	96
Overdrawing Built-in Function Graphs	97
Graphing Manually Entered Functions	97
Overdrawing Manually Input Graphs	97
Specifying the Graph Range	98
8-3 Polar Coordinate Graphs	98
Graphing Built-In Scientific Functions	98
Graphing Manually Entered Functions	98
Specifying the Graph Range	99
8-4 Parametric Graphs	99
Specifying the Graph Range	100
8-5 Inequality Graphs	100
Overdrawing Inequality Graphs	101
Specifying the Graph Range	101
8-6 Integration Graphs	101
8-7 Probability Distribution Graphs	102
8-8 Single-Variable Statistical Graphs	103
8-9 Paired-Variable Statistical Graphs	105
8-10 Storing Functions in Memory	106
Accessing the Graphic Function Memory	106
Graph Function Types	106
Editing Graph Functions in Memory	108
Drawing Graphs from Memory	108
Specifying the Graphs to be Drawn	108
Function Linking	109
8-11 Graph Solve	110
Displaying the Graph Solve Menu	110
Determining Roots	111
Determining Maximums and Minimums	112
Determinig y-intercepts	112
Determining Points of Intersection for Two Graphs	112
Determining a Coordinate ( x for a given y/y for a given x)	113
Determining the Derivative for a Given Point	114
8-12 Other Graph Functions	115
Setting the Type of Graphing Method	115
Trace Function	115
Scrolling Graphs	117
Notes on Using the Trace Function	117
Plot Function	118
Line Function	120
Graph Scroll Function	121
Zoom Functions	122
Before Using Zoom	122
Box Zoom Function	122
Using the Factor Zoom Function to Enlarge and Reduce the Entire Graph	123
Auto Range	126
Graph Adjust	127
Coordinate Rounding	128
Using the Overwrite Function	128
8-13 Some Graphing Examples	129
Chapter 9 Dual Graph	130
9-1 Before Using Dual Graph	131
About Dual Graph Screen Types	131
9-2 Specifying the Left and Right Display Range Parameters	131
9-3 Drawing a Graph in the Active Screen	132
9-4 Displaying a Graph in the Inactive Screen	133
Before Displaying a Graph in the Inactive Screen	133
Copying the Active Graph to the Inactive Screen	133
Switching the Contents of the Active and Inactive Screens	134
Drawing Different Graphs on the Active Screen and Inactive Screen	134
Other Graph Functions with Dual Graph	135
Chapter 10 Dynamic Graphing	137
10-1 Before Using the Dynamic Graph Mode	138
10-2 Inputting a New Equation	138
10-3 Editing a Function	139
10-4 Deleting a Function	139
10-5 Drawinig a Dynamic Graph	140
1O-time Continuous Drawing	141
Continuous Drawing	142
Stop & Go Drawing	143
Overwriting	143
Function Linking	144
Chapter 11 Table and Graph Mode	145
11-1 Entering the Table and Graph Mode	146
11-2 Generating a Table and Drawing a Graph for a Function	146
Storing a Function and Generating a Numeric Table	146
Editing a Function	149
Function Linking	150
Editing a Table List	150
Deleting List Area Contents	151
Editing Function and Table Data	151
Row Operations	152
Drawing a Graph Using Table Data	153
Before Drawing a Graph	153
Specifying the Graphs to be Drawn	153
11-3 Using the Table and Graph Mode with a Recursion Formula	154
Editing Table Data	156
Drawing a Graph Using Table Data	157
Specifying the Y-Axis and. X-Axis for the Graph	157
Chapter 12 Program/File Editor Mode	158
12-1 Before Using the Program/File Editor Mode	159
12-2 Using the Program Mode	159
Entering the Program Mode	159
Specifying the Calculation Mode	159
Selecting a Program Area	160
Checking How Much Memory Is Used by a program	160
Inputting a Program	160
Executing a Program Stored in Memory	160
12-3 Deleting Programs	161
12-4 Error Messages	162
12-5 Counting the Number of Bytes	162
Checking the Amount of Memory Remaining	162
Checking Where the Cursor Is Currently Located	162
12-6 Using the File Editor Mode	162
Entering the File Editor Mode	162
Password Protection	163
Inputting Data into a File	164
Inputting Program Commands	164
Inputting Upper-Case and Lower-Case Alpha Characters	164
Inputting Symbols	164
Executing a Program	165
Checking the Memory Used by a Program	166
Searching for Files	166
Searching for Data in a File	167
Editing File Data	168
Other Useful Cursor Movement Functions	169
12-7 Program Commands	169
Displaying the Program Function Menu	169
About the Newline Funtction	169
Displaying the Jump Command Menu	169
Displaying the Relational Operator Menu	170
Displaying the Punctuation Symbol Menu	170
12-8 Using Jump Commands	170
About Unconditional Jumps	170
About Conditional Jumps	171
About Count Jumps	171
12-9 Using Subroutines	172
Subroutines Save Memory	172
12-10 Using Array Memory	172
Array Memories to Simplify Programming	173
Cautions When Using Array Memories	173
Sample Programs That Use Array Memory	173
12-11 Displaying Text Messages	174
12-12 Using Matrices in Programs	175
12-13 Using the Graph Function in Programs	176
Chapter 13 Data Communications	177
13-1 Connecting Two CFX-980OG Units	178
13-2 Connecting the CFX-9800G with a Personal Computer	178
13-3 Connecting the CFX-9800G to a CASIO Label Printer	178
13-4 Before Starting Data Communications	179
Entering the LINK Mode	179
About the Data Type Selection Screen	179
13-5 Setting Communications Parameters	180
Setting CFX-9800G Parameters	180
13-6 Using ALL, Range, and Factor	181
13-7 Using Program, Function Mem, Matrix, and Graph Function	182
13-8 Using Editor	183
13-9 ,Using Statistics, Variable Mem, Table, and Equation	185
13-10 Using Dynamic Graph	187
13-11 Using Back Up to Send All Mode Settings and Memory Data	188
13-12 Screen Copy Function	189
To Copy the Screen	189
13-13 Data Communications Precautions	190
Appendix	190
Appendix A Power Supply	191
When to Replace Batteries	191
Replacing Batteries	191
About the Auto Power Off Function	192
Appendix B To Reset the Calculator	192
Appendix C Function Reference	193
Manual Calculations	193
Program Calculations	196
Appendix D Error Message Table	197
Appendix E Input Ranges	198
Appendix F Specifications	200
Index	202

Match case Limit results 1 per page

Chapter

Differential,

Integration,

and

Calculations

3.1

How

the Unit

Calculates

Differentials

The

following

the

input

format

for

differentials:

Elf(x)MalAxID

Increase/decrease

Point

for

which

you

want

determine

the

derivative

tildx(f(x),

Ax)

f(a)

The

differentiation

for

this

type

calculation

defined

as:

f(a)=Iim

f(a+

Ax)—f(a)

—t0

this

definition,

infinitesimal

replaced

sufficiently

small

Ax,

with

the

value

the

neighborhood

(a)

calculated

as:

(a)=

f(a

Ax)—

f(a)

order

provide

the

best

precision

possible,

this

unit

employs

central

difference

per-

form

differential

calculations.

The

following

illustrates

central

difference.

f(x)

f(a

Ax)—f(a—

Ax)

2Ax

a—

a+Ax

The

slopes

point

and

point

Ax,

and

point

and

point

—

function

y=f(x)

are

follows:

f(a

Ax)—

f(a)

f(a)—f(a-

Ax)

the

above,

Ay/Ax

called

the

forward

difference,

while.

Vy/Vx

the

backward

difference.

calculate

derivatives,

the

unit

takes

the

average

between

the

value

Ay/Axand

Vyl,Vx,

thereby

providing

higher

precision

for

derivatives.

This

average,

which

called

the

central

difference,

expressed

as:

(f(a+

ox)-f(a)

f(a)-f(a—

Ax))

_f(a+

Ax)—f(a-

Ax)

2A.Y

•To

Perform

Differential

Calculation

determine

the

derivative

point

x=3

for

the

function

x-6,

when

the

increase/decrease

xis:

defined

dx=

—5.

Example

Input

the

function

f(x).

123

uzenEEMEMEI

Input

point

for

whiCh

you

want

determine

the

derivative.

Input

Ax,

which

the

increase/

decrease

CIODMITI

3+4X

- 1

clx<X"3+4X

- 1

d/d71

,3,gX-1‘5_

+4X 2+X-1

- 6

)

•X

the

only

expression

that

can

used

the

function

x).

you

use

any

other

varia-

ble

name

through

0),

that

variable

name

regarded

constant,

using

the

current

contents

the

corresponding

value

memory

the

calculation.

*Input

for

the

increase/decrease

can

skipped.

When

you

do,

the

unit

auto-

matically

uses

value

for

that

appropriate

for

the

value

which

you

speci-

fied

the

point

for

which

you

wanted

determine

the

derivative.

•In

general,

calculation

precision

±1

the

least

significant

digit

the

result.

—