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Casio FX-9750GII-SC User Guide - Page 62

Differential Calculations, Using Differential Calculation in a Graph Function - derivative

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I Differential Calculations [OPTN]-[CALC]-[d/dx] To perform differential calculations, first display the function analysis menu, and then input the values using the syntax below. *(CALC)* (d/dx) f(x)atol * fx-7400GII: (CALC) (a: point for which you want to determine the derivative, tol: tolerance) d/dx(f(x) a) d dx f(a) The differentiation for this type of calculation is defined as: f ' (a) = Alixm0-f-(-a-+-A-A-xx)----f-(-a-) In this definition, infinitesimal is replaced by a sufficiently small x, with the value in the neighborhood of f' (a) calculated as: f (a + Ax) - f (a) f' (a) ------A-x------ In order to provide the best precision possible, this unit employs central difference to perform differential calculations. Example To determine the derivative at point x = 3 for the function y = x3 + 4x2 + x - 6, with a tolerance of "tol" = 1E - 5 Input the function f(x). *(CALC)* (d/dx)T,B CTV T E * fx-7400GII: (CALC) Input point x = a for which you want to determine the derivative. B Input the tolerance value. @$ DU Using Differential Calculation in a Graph Function • Omitting the tolerance (tol) value when using the differential command inside of a graph function simplifies the calculation for drawing the graph. In such a case, precision is sacrificed for the sake of faster drawing. The tolerance value is specified, the graph is drawn with the same precision obtained when you normally perform a differential calculation. • You can also omit input of the derivative point by using the following format for the differential graph: Y2=d/dx(Y1). In this case, the value of the X variable is used as the derivative point. Differential Calculation Precautions • In the function f(x), only X can be used as a variable in expressions. Other variables (A through Z excluding X, r, Ƨ) are treated as constants, and the value currently assigned to that variable is applied during the calculation. • Input of the tolerance (tol) value and the closing parenthesis can be omitted. If you omit tolerance (tol) value, the calculator automatically uses a value for tol as 1E-10. • Specify a tolerance (tol) value of 1E-14 or greater. An error (Time Out) occurs whenever no solution that satisfies the tolerance value can be obtained. • Pressing during calculation of a differential (while the cursor is not shown on the display) interrupts the calculation. 2-24

Section	Page
Contents	3
Getting Acquainted — Read This First!	6
Chapter 1 Basic Operation	8
1. Keys	8
2. Display	9
3. Inputting and Editing Calculations	12
4. Using the Math Input/Output Mode	17
5. Option (OPTN) Menu	29
6. Variable Data (VARS) Menu	30
7. Program (PRGM) Menu	32
8. Using the Setup Screen	33
9. Using Screen Capture	36
10. When you keep having problems...	37
Chapter 2 Manual Calculations	39
1. Basic Calculations	39
2. Special Functions	44
3. Specifying the Angle Unit and Display Format	48
4. Function Calculations	49
5. Numerical Calculations	59
6. Complex Number Calculations	68
7. Binary, Octal, Decimal, and Hexadecimal Calculations with Integers	71
8. Matrix Calculations	74
9. Metric Conversion Calculations	86
Chapter 3 List Function	90
1. Inputting and Editing a List	90
2. Manipulating List Data	94
3. Arithmetic Calculations Using Lists	99
4. Switching Between List Files	102
Chapter 4 Equation Calculations	103
1. Simultaneous Linear Equations	103
2. High-order Equations from 2nd to 6th Degree	104
3. Solve Calculations	106
Chapter 5 Graphing	107
1. Sample Graphs	107
2. Controlling What Appears on a Graph Screen	108
3. Drawing a Graph	112
4. Storing a Graph in Picture Memory	116
5. Drawing Two Graphs on the Same Screen	117
6. Manual Graphing	118
7. Using Tables	121
8. Dynamic Graphing	126
9. Graphing a Recursion Formula	128
10. Graphing a Conic Section	133
11. Changing the Appearance of a Graph	133
12. Function Analysis	135
Chapter 6 Statistical Graphs and Calculations	141
1. Before Performing Statistical Calculations	141
2. Calculating and Graphing Single-Variable Statistical Data	144
3. Calculating and Graphing Paired-Variable Statistical Data	149
4. Performing Statistical Calculations	155
5. Tests	162
6. Confidence Interval	175
7. Distribution	178
8. Input and Output Terms of Tests, Confidence Interval, and Distribution	190
9. Statistic Formula	193
Chapter 7 Financial Calculation (TVM)	196
1. Before Performing Financial Calculations	196
2. Simple Interest	197
3. Compound Interest	198
4. Cash Flow (Investment Appraisal)	200
5. Amortization	202
6. Interest Rate Conversion	204
7. Cost, Selling Price, Margin	205
8. Day/Date Calculations	206
9. Depreciation	207
10. Bond Calculations	209
11. Financial Calculations Using Functions	211
Chapter 8 Programming	212
1. Basic Programming Steps	212
2. PRGM Mode Function Keys	213
3. Editing Program Contents	214
4. File Management	216
5. Command Reference	218
6. Using Calculator Functions in Programs	232
7. PRGM Mode Command List	248
8. Program Library	253
Chapter 9 Spreadsheet	255
1. Spreadsheet Basics and the Function Menu	255
2. Basic Spreadsheet Operations	256
3. Using Special S • SHT Mode Commands	268
4. Drawing Statistical Graphs, and Performing Statistical and Regression Calculations	269
5. S • SHT Mode Memory	274
Chapter 10 eActivity	276
1. eActivity Overview	276
2. eActivity Function Menus	277
3. eActivity File Operations	278
4. Inputting and Editing Data	279
Chapter 11 Memory Manager	289
1. Using the Memory Manager	289
Chapter 12 System Manager	300
1. Using the System Manager	300
2. System Settings	300
Chapter 13 Data Communications	304
1. Connecting Two Units	304
2. Connecting the Calculator to a Personal Computer	304
3. Performing a Data Communication Operation	305
4. Data Communications Precautions	308
5. Screen Image Send	314
Chapter 14 Using SD Cards (fx-9860G SD only)	318
1. Using an SD Card	318
2. Formatting an SD Card	320
3. SD Card Precautions during Use	320
Appendix	321
1. Error Message Table	321
2. Input Ranges	325
E-CON2 Application	327
1 E-CON2 Overview	329
2 Using the Setup Wizard	330
3 Using Advanced Setup	340
4 Using a Custom Probe	354
5 Using the MULTIMETER Mode	360
6 Using Setup Memory	361
7 Using Program Converter	365
8 Starting a Sampling Operation	370
9 Using Sample Data Memory	373
10 Using the Graph Analysis Tools to Graph Data	376
11 Graph Analysis Tool Graph Screen Operations	380

Match case Limit results 1 per page

2-24

Differential Calculations

[OPTN]

[CALC]

[

]

To perform differential calculations, first display the function analysis menu, and then input the

values using the syntax below.

(CALC)*

(

)

(

)

tol

* fx-7400G

(CALC)

(

: point for which you want to determine the derivative,

tol

: tolerance)

The differentiation for this type of calculation is defined as:

In this definition,

infinitesimal

is replaced by a

sufficiently small

, with the value in the

neighborhood of

(

) calculated as:

In order to provide the best precision possible, this unit employs central difference to perform

differential calculations.

Example

To determine the derivative at point

= 3 for the function

– 6, with a tolerance of “

tol

”=1

–5

Input the function

(

(CALC)*

(

)

* fx-7400G

(CALC)

Input point

for which you want to determine the derivative.

Input the tolerance value.

Using Differential Calculation in a Graph Function

• Omitting the tolerance (

tol

) value when using the differential command inside of a graph

function simplifies the calculation for drawing the graph. In such a case, precision is

sacrificed for the sake of faster drawing.The tolerance value is specified, the graph is drawn

with the same precision obtained when you normally perform a differential calculation.

• You can also omit input of the derivative point by using the following format for the differential

graph:Y2=

(Y1). In this case, the value of the X variable is used as the derivative point.

Differential Calculation Precautions

• In the function

(

), only X can be used as a variable in expressions. Other variables

(A through Z excluding X,

) are treated as constants, and the value currently assigned to

that variable is applied during the calculation.

• Input of the tolerance (

tol

) value and the closing parenthesis can be omitted. If you omit

tolerance (

tol

) value, the calculator automatically uses a value for

tol

as 1

–10.

• Specify a tolerance (

tol

) value of 1

–14 or greater. An error (Time Out) occurs whenever no

solution that satisfies the tolerance value can be obtained.

• Pressing

during calculation of a differential (while the cursor is not shown on the display)

interrupts the calculation.

(

)

(

)

(

)

(

)

(

)–

(

)

(

) = lim

–––––––––––––

(

)–

(

)

(

) = lim

–––––––––––––

(

)–

(

)

(

)

–––––––––––––

(

)–

(

)

(

)

–––––––––––––