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HP hp39gPlus User Guide - Page 165

Finding derivatives

UPC - 829160013138

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Symbolic calculations in the Function aplet You can perform symbolic operations in the Function aplet's Symbolic view. For example, to find the derivative of a function in the Function aplet's Symbolic view, you define two functions and define the second function as a derivative of the first function. You then evaluate the second function. See "To find derivatives in the Function aplet's Symbolic view" on page 11-22 for an example. Finding derivatives The hp 39g+ can perform symbolic differentiation on some functions. There are two ways of using the hp 39g+ to find derivatives. • You can perform differentiations in HOME by using the formal variables, S1 to S5. • You can perform differentiations of functions of X in the Function aplet. To find derivatives in HOME To find the derivative of the function in HOME, use a formal variable in place of X. If you use X, the differentiation function substitutes the value that X holds, and returns a numeric result. For example, consider the function: dx( sin (x 2 ) + 2 cos (x) ) 1. Enter the differentiation function onto the command line, substituting S1 in place of X. S1 S1 2 S1 2. Evaluate the function. Using mathematical functions 11-21

Section	Page
Manual conventions	9
Notice	10
1	11
On/off, cancel operations	11
To turn on	11
To cancel	11
To turn off	11
The display	12
To adjust the contrast	12
To clear the display	12
Parts of the display	12
NOTE	12
Annunciator	13
Description	13
The keyboard	13
Menu keys	13
Aplet control keys	14
Key	14
Meaning	14
Entry/Edit keys	15
Key	15
Meaning (Continued)	15
Shifted keystrokes	16
Key	16
Description	16
HELPWITH	17
Example	17
Math keys	17
.	17
HINT	18
Program commands	18
Inactive keys	18
Menus	18
To search a menu	18
To cancel a menu	19
Input forms	19
Reset input form values	19
Mode settings	20
HINT	20
Setting	20
Options	20
Setting a mode	22
HINT	22
Aplets (E-lessons)	22
Aplet name	23
Use this aplet to explore:	23
Quad Explorer aplet	24
HINT	24
Trig Explorer aplet	25
Aplet library	26
To open an aplet	26
Aplet views	26
Symbolic view	26
Plot view	27
Numeric view	27
Plot-Table view	27
Plot-Detail view	27
Overlay Plot view	28
Note view	28
Sketch view	28
Aplet view configuration	28
Plot Setup	28
Numeric Setup	29
Symbolic Setup	29
To change views	29
To save aplet configuration	29
Mathematical calculations	29
Where to start	29
Entering expressions	29
Example	30
Long results	30
Negative numbers	30
Scientific notation (powers of 10)	30
Example	30
Explicit and implicit multiplication	31
HINT	31
Parentheses	31
Entering...	31
Calculates...	31
Algebraic precedence order of evaluation	32
Largest and smallest numbers	32
Clearing numbers	32
Using previous results	32
To copy a previous line	33
To reuse the last result	33
To repeat a previous line	33
Example	33
HINT	34
Storing a value in a variable	34
Accessing the display history	35
Key	35
Function	35
Clearing the display history	35
Using fractions	35
Setting Fraction mode	35
Setting fraction precision	36
Fraction calculations	37
Converting decimals to fractions	38
Complex numbers	39
Complex results	39
To enter complex numbers	39
Storing complex numbers	39
Catalogs and editors	40
Catalog/Editor	40
Contents	40
Aplet library ()	40
Aplets.	40
Sketch editor ( sketch)	40
Sketches and diagrams, See Chapter 15, “Notes and sketches”.	40
List ( list)	40
Lists. In HOME, lists are enclosed in {}. See Chapter 14, “Lists”.	40
Matrix ( matrix)	40
One- and two-dimensional arrays. In HOME, arrays are enclosed in []. See Chapter 13, “Matrices”.	40
Notepad ( notepad)	40
Notes (short text entries). See Chapter 15, “Notes and sketches”.	40
Program ( progrm)	40
Programs that you create, or associated with user-defined aplets. See Chapter 16, “Programming”.	40
2	41
Aplet views	41
About the Symbolic view	41
Defining an expression (Symbolic view)	41
Evaluating expressions	43
In aplets	43
In HOME	44
SYMB view keys	44
Key	44
Meaning	44
About the Plot view	45
Setting up the plot (Plot view setup)	45
Plot view settings	46
Field	46
Meaning	46
Field	46
Meaning	46
Reset plot settings	47
Exploring the graph	47
PLOT view keys	47
Key	47
Meaning	47
Trace a graph	48
To move between relations	48
To jump directly to a value	49
To turn trace on/off	49
Zoom within a graph	49
ZOOM options	49
Option	49
Meaning	49
Center	49
Box...	49
In	49
Out	49
X-Zoom In	49
X-Zoom Out	49
Y-Zoom In	50
Y-Zoom Out	50
Square	50
Set Factors...	50
Auto Scale	50
Decimal	50
Integer	50
Trig	50
Un-zoom	51
ZOOM examples	51
To box zoom	52
To set zoom factors	53
Other views for scaling and splitting the graph	54
VIEWS menu options	54
Option	54
Meaning	54
Plot- Detail	54
Plot-Table	54
Overlay Plot	54
Auto Scale	54
Decimal	54
Integer	54
Trig	55
Split the screen	55
Overlay plots	56
Decimal scaling	56
Integer scaling	56
Trigonometric scaling	56
About the numeric view	56
Setting up the table (Numeric view setup)	57
Numeric view settings	57
Field	57
Meaning	57
Reset numeric settings	58
Exploring the table of numbers	58
NUM view menu keys	58
Key	58
Meaning	58
Zoom within a table	58
ZOOM options	58
Option	58
Meaning	58
HINT	59
Automatic recalculation	59
Building your own table of numbers	59
Build a table	59
Clear data	60
“Build Your Own” menu keys	60
Key	60
Meaning	60
clear	60
Example: plotting a circle	61
3	63
About the Function aplet	63
Getting started with the Function aplet	63
Open the Function aplet	63
Define the expressions	64
Set up the plot	64
Plot the functions	64
Change the scale	65
Trace a graph	65
Analyse graph with FCN functions	66
To find a root of the quadratic function	66
To find the intersection of the two functions	66
To find the slope of the quadratic function	67
To find the signed area of the two functions	67
To find the extremum of the quadratic	68
HINT	69
Display the numeric view	69
Set up the table	69
Explore the table	69
To navigate around a table	70
To go directly to a value	70
To access the zoom options	70
To change font size	70
To display the symbolic definition of a column	70
Function aplet interactive analysis	71
Access FCN variables	71
FCN functions	72
Function	72
Description	72
Shading area	73
Plotting a piecewise-defined function	74
4	75
About the Parametric aplet	75
Getting started with the Parametric aplet	75
Open the Parametric aplet	75
Define the expressions	75
Set angle measure	76
Set up the plot	76
Plot the expression	76
Overlay plot	77
Display the numbers	77
5	79
Getting started with the Polar aplet	79
Open the Polar aplet	79
Define the expression	79
Specify plot settings	79
Plot the expression	79
Explore the graph	80
Display the numbers	80
6	81
About the Sequence aplet	81
Getting started with the Sequence aplet	81
Open the Sequence aplet	81
Define the expression	82
Specify plot settings	82
Plot the sequence	82
Display the table	83
7	85
About the Solve aplet	85
Getting started with the Solve aplet	86
Open the Solve aplet	86
Define the equation	86
Enter known variables	86
HINT	87
Solve the unknown variable	87
Plot the equation	87
Solve aplet’s NUM view keys	88
Key	88
Meaning	88
Use an initial guess	89
HINT	89
Number format	89
Interpreting results	90
Message	90
Condition	90
The initial guess lies outside the domain of the equation. Therefore, the solution was not a real...	91
The value of the equation is the same at every point sampled.	91
HINT	91
The Root-Finder at work	91
Plotting to find guesses	91
Using variables in equations	94
Home variables	94
HINT	94
Aplet variables	94
8	95
About the Statistics aplet	95
Getting started with the Statistics aplet	95
Advertising minutes (independent, x)	95
Resulting Sales ($) (dependent, y)	95
2	95
1400	95
1	95
920	95
3	95
1100	95
5	95
2265	95
5	95
2890	95
4	95
2200	95
Open the Statistics aplet	96
Enter data	96
Choose fit and data columns	97
Explore statistics	97
Setup plot	98
Plot the graph	98
Draw the regression curve	98
Display the equation for best linear fit	98
Predict values	99
Entering and editing statistical data	100
HINT	100
Statistics aplet’s NUM view keys	100
Key	100
Meaning	100
Example	101
Key	102
Meaning	102
Height (cm)	103
Frequency	103
160	103
5	103
165	103
3	103
170	103
8	103
175	103
2	103
180	103
1	103
Save data	104
Edit a data set	105
Delete data	105
Insert data	105
Sort data values	105
Defining a regression model	106
Angle Setting	106
To choose the fit	106
Fit models	106
Fit model	106
Meaning	106
To define your own fit	107
Computed statistics	107
One-variable	107
Statistic	107
Definition	107
Two-variable	108
Statistic	108
Definition	108
Plotting	109
To plot statistical data	109
Plot types	110
Histogram	110
Box and Whisker Plot	110
Scatter Plot	110
Fitting a curve to 2VAR data	111
Correlation coefficient	111
Relative Error	111
HINT	112
Setting up the plot (Plot setup view)	112
Plot type (1VAR)	112
Histogram width	112
Histogram range	112
Plotting mark (2VAR)	112
Connected points (2VAR)	112
Trouble-shooting a plot	112
Exploring the graph	113
Statistics aplet’s PLOT view keys	113
Key	113
Meaning	113
Calculating predicted values	114
Find predicted values	114
HINT	115
9	117
About the Inference aplet	117
Example data	117
Getting started with the Inference aplet	117
Open the Inference aplet	117
Inference aplet’s SYMB view keys	118
Hypothesis Tests	118
Confidence Intervals	118
Select the inferential method	119
Enter data	119
Field name	119
Definition	119
Display on-line help	120
Display test results in numeric format	120
Plot test results	120
Importing sample statistics from the Statistics aplet	120
Open the Statistics aplet	121
Enter data	121
HINT	121
Calculate statistics	121
Open Inference aplet	122
Select inference method and type	122
Set up the interval calculation	122
Import the data	123
Display Numeric view	123
Display Plot view	123
Hypothesis tests	124
One-Sample Z-Test	124
Menu name	124
Inputs	124
Field name	124
Definition	124
Results	125
Result	125
Description	125
Test Z	125
Prob	125
Critical Z	125
Critical	125
Two-Sample Z-Test	125
Menu name	125
Inputs	125
Field name	125
Definition	125
Results	126
Result	126
Description	126
One-Proportion Z-Test	126
Menu name	126
Inputs	127
Field name	127
Definition	127
Results	127
Result	127
Description	127
Two-Proportion Z-Test	127
Menu name	127
Inputs	128
Field name	128
Definition	128
Results	128
Result	128
Description	128
One-Sample T-Test	128
Menu name	128
Inputs	129
Field name	129
Definition	129
Results	129
Result	129
Description	129
Two-Sample T-Test	130
Menu name	130
Inputs	130
Field name	130
Definition	130
Results	131
Result	131
Description	131
Confidence intervals	131
One-Sample Z-Interval	131
Menu name	131
Inputs	131
Field name	131
Definition	131
Results	132
Result	132
Description	132
Two-Sample Z-Interval	132
Menu name	132
Inputs	132
Field name	132
Definition	132
Results	132
Result	132
Description	132
One-Proportion Z-Interval	133
Menu name	133
Inputs	133
Field name	133
Definition	133
Results	133
Result	133
Description	133
Two-Proportion Z-Interval	133
Menu name	133
Inputs	133
Field name	133
Definition	133
Results	134
Result	134
Description	134
One-Sample T-Interval	134
Menu name	134
Inputs	134
Field name	134
Definition	134
Results	135
Result	135
Description	135
Two-Sample T-Interval	135
Menu name	135