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14-26 Computer Algebra System (CAS)
You must be in Rigorous (not Sloppy) mode to apply
SERIES with unidirectional expansion. (See “CAS modes”
on page 14-5 for instructions on setting and changing
modes.
Example 1
Give a 3rd-order expansion of in the vicinity of
x = 0
+
.
Typing:
gives:
Example 2
Give a 3rd-order expansion of in the vicinity of
x = 0
–
.
Typing:
gives:
Note that h = –x is positive as x → 0
–
.
Example 3
If you enter the order as an integer rather than a real, as
in:
you will get the following error:
SERIES Error: Unable to find sign.
Note that if you had been in Sloppy rather than Rigorous
mode, all three examples above would have returned the
same answer as you got when exploring in the vicinity of
x = 0
+
:
x
2
x
3
+
SERIES X
2
X
3
+ X 03.0,=,()
1
16
------
h
4
⋅
1–
8
------
h
3
⋅
1
2
---
h
2
⋅ h+++0h
5
()+ hx=()
x
2
x
3
+
S
ERIES X
2
X
3
+ X 03.0–,=,(
)
1–
16
------
h
4
⋅
1–
8
------
h
3
⋅
1–
2
------
h
2
⋅ h 0 h
5
()++++ hx–=()
SERIES X
2
X
3
+ X 03,=,()
hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM
- HP 40gs graphing calculator 1
- Printing History 2
- Contents 3
- 12 Using the Finance Solver 5
- 15 Equation Writer 6
- 22 Extending aplets 8
- Manual conventions 11
- Getting started 13
- The display 14
- The keyboard 15
- Menu keys 16
- Aplet control keys 16
- Entry/Edit keys 17
- Shifted keystrokes 18
- Getting started 1-7 19
- Program 20
- Input forms 21
- Mode settings 22
- Setting a mode 23
- Aplets (E-lessons) 24
- Quad Explorer 26
- Getting started 1-15 27
- Aplet library 28
- Aplet views 28
- Overlay Plot 29
- Aplet view configuration 30
- Mathematical calculations 31
- Example Calculate : 32
- Example Calculate 32
- Getting started 1-21 33
- Last output 34
- Last input 34
- Edit line 34
- Getting started 1-23 35
- Storing a value 36
- Using fractions 37
- Setting fraction 38
- Fraction 39
- Converting 40
- Complex numbers 41
- Catalogs and editors 42
- Aplets and their views 43
- 2-2 Aplets and their views 44
- Evaluating expressions 45
- 2-4 Aplets and their views 46
- About the Plot view 47
- Plot view 48
- To move between 50
- Zoom within a 51
- 2-10 Aplets and their views 52
- Aplets and their views 2-11 53
- 2-12 Aplets and their views 54
- VIEWS menu 55
- 2-14 Aplets and their views 56
- Trigonometric 57
- About the numeric view 58
- Reset numeric 59
- NUM view 59
- NUM), choose 61
- CLEAR) 61
- “Build Your Own” menu keys 62
- Example: plotting a circle 62
- SETUP-NUM 63
- Function aplet 65
- Define the 66
- Plot the 66
- Change the 67
- Analyse graph 68
- Function aplet 3-5 69
- To find the 70
- Display the 71
- Explore the 71
- 3-8 Function aplet 72
- Access FCN 73
- 3-10 Function aplet 74
- Function aplet 3-11 75
- CLEAR to clear all lines.) 76
- CHARS ≤ 76
- CHARS > 1 76
- AND CHARS ≤ 1 76
- Parametric aplet 77
- Set angle 78
- Polar aplet 81
- and R1 82
- Sequence aplet 83
- Solve aplet 87
- 7-2 Solve aplet 88
- Solve the 89
- Solve aplet’s NUM view keys 90
- Use an initial guess 91
- Interpreting results 92
- Plotting to find guesses 93
- 7-8 Solve aplet 94
- Solve aplet 7-9 95
- Using variables in equations 96
- Linear Solver aplet 97
- Define and 98
- Linear Solver aplet 8-3 99
- Triangle Solve aplet 101
- 9-2 Triangle Solve aplet 102
- Errors No solution with 103
- Statistics aplet 105
- Open the 106
- Choose fit and 107
- SETUP-PLOT 108
- Statistics aplet 10-5 109
- 10-6 Statistics aplet 110
- Statistics aplet 10-7 111
- 10-8 Statistics aplet 112
- CLEAR is used the 113
- Sort data 115
- Defining a regression model 116
- To define your 117
- Computed statistics 118
- Plotting You can plot: 119
- Plot types 120
- Fitting a curve to 2VAR data 121
- SETUP-PLOT) sets most of the 122
- Trouble-shooting a plot 123
- Exploring the graph 123
- Calculating predicted values 124
- Statistics aplet 10-21 125
- Inference aplet 127
- 11-2 Inference aplet 128
- Select the 129
- 11-4 Inference aplet 130
- Calculate 131
- 11-6 Inference aplet 132
- Display Numeric 133
- Display Plot 133
- Hypothesis tests 134
- Two-Sample Z-Test 135
- One-Proportion Z-Test 136
- Two-Proportion Z-Test 137
- One-Sample T-Test 138
- Inputs The inputs are: 139
- Results The results are: 139
- Two-Sample T-Test 140
- Confidence intervals 141
- Two-Sample Z-Interval 142
- One-Proportion Z-Interval 143
- Two-Proportion Z-Interval 143
- One-Sample T-Interval 144
- Two-Sample T-Interval 145
- Using the Finance Solver 147
- Background 147
- 12-2 Using the Finance Solver 148
- Using the Finance Solver 12-3 149
- Performing TVM calculations 150
- Example 1 - Loan calculations 151
- 12-6 Using the Finance Solver 152
- Calculating Amortizations 153
- 12-8 Using the Finance Solver 154
- Using mathematical functions 155
- Math functions by category 156
- Keyboard functions 157
- ASIN Arc sine: sin 158
- Takes the nth root of x 160
- Complex number functions 161
- Constants 162
- Conversions 162
- Hyperbolic trigonometry 163
- List functions 164
- Loop functions 164
- Matrix functions 165
- Polynomial functions 165
- Probability functions 166
- Real-number functions 168
- Two-variable statistics 171
- Symbolic functions 171
- Test functions 173
- Symbolic calculations 174
- Finding derivatives 175
- To find derivatives 176
- − XXS ,53,1,0 177
- Program constants 179
- Physical constants 179
- Computer Algebra System (CAS) 183
- An example 184
- CAS variables 186
- CAS modes 187
- Using CAS functions in HOME 189
- Online Help 190
- ALGB menu 192
- EXPAND Distributivity 194
- FACTOR Factorization 194
- QUOTE Quoted expression 195
- UNASSIGN Clear a variable 197
- DIFF menu 198
- ≠0), and a whole number n 199
- IBP Partial integration 200
- PREVAL Evaluate a primitive 205
- SERIES Limited 206
- TABVAR Variation table 209
- REWRI menu 210
- EPSX0 Disregard small values 211
- FDISTRIB Distributivity 212
- POWEXPAND Transform a power 213
- SIMPLIFY Simplify 214
- XNUM Evaluation of reals 214
- XQ Rational approximation 214
- SOLV menu 215
- The zeros of an expression 216
- LINSOLVE Solve linear system 217
- SOLVE Solve equations 219
- Solve systems 219
- TRIG menu 220
- TRIG Simplify using sin(x) 225
- Simplify using the cosines 226
- Simplify using the sines 226
- Simplify using the tangents 226
- Algebra menu 227
- Complex menu 227
- Constant menu 228
- Diff & Int menu 228
- Hyperb menu 228
- Integer menu 228
- MOD See “MOD” on page 13-15 232
- Modular menu 233
- Polynomial menu 237
- Real menu 242
- Rewrite menu 242
- Solve menu 242
- Tests menu 243
- Trig menu 243
- Equation Writer 253
- 15-2 Equation Writer 254
- Configuration menus 255
- Equation Writer 15-5 257
- 15-6 Equation Writer 258
- More Examples Example1 259
- 15-8 Equation Writer 260
- Equation Writer 15-9 261
- Changing the 262
- How to modify an expression 263
- Accessing CAS functions 264
- How to enter infix 265
- How to enter prefix 265
- 15-14 Equation Writer 266
- Equation Writer 15-15 267
- Equation Writer variables 268
- Equation Writer 15-17 269
- SHIFT MATH keys The key 270
- SHIFT SYMB or 271
- SHIFT HOME keys 271
- PLOT key Pressing in the 271
- 15-20 Equation Writer 272
- Equation Writer 15-21 273
- Step-by-Step Examples 275
- Example 2 Given that 276
- Step-by-Step Examples 16-3 277
- 16-4 Step-by-Step Examples 278
- Step-by-Step Examples 16-5 279
- 16-6 Step-by-Step Examples 280
- First method Type: 281
- Step-by-Step Examples 16-9 283
- Step-by-Step Examples 16-11 285
- Exercise 7 287
- Part 1 First go to CAS MODES 288
- Step-by-Step Examples 16-15 289
- 16-16 Step-by-Step Examples 290
- Part 3 Calculate by typing: 291
- You can now define the 291
- Part 4 To calculate , begin 292
- Step-by-Step Examples 16-19 293
- 16-20 Step-by-Step Examples 294
- Step-by-Step Examples 16-21 295
- Press to get the 297
- Step-by-Step Examples 16-27 301
- Step-by-Step Examples 16-29 303
- Introduction 305
- To store the results 306
- To use variables in 307
- The VARS menu 308
- To access an aplet 312
- Memory Manager 313
- Matrices 315
- Creating and storing matrices 316
- MATRIX to see the Matrix 317
- Working with matrices 318
- To display one 319
- To create a matrix 319
- Matrix arithmetic 320
- Matrices 18-7 321
- To divide by a 322
- To negate each 322
- Matrices 18-9 323
- Matrix functions and commands 324
- Matrices 18-11 325
- 18-12 Matrices 326
- Examples 327
- Reduced-Row 328
- Echelon Form 328
- Matrices 18-15 329
- Create a list in 331
- CLEAR Clears all lists 332
- Displaying and editing lists 334
- To insert an element 335
- To store one 335
- Lists 19-7 337
- 19-8 Lists 338
- Lists 19-9 339
- 19-10 Lists 340
- Notes and sketches 341
- Note edit keys 342
- Aplet sketch view 343
- DRAW keys 344
- Notes and sketches 20-5 345
- The notepad 346
- Notepad Catalog keys 347
- NOTEPAD), open the note 348
- Programming 349
- Program catalog 350
- Program catalog keys 351
- Creating and editing programs 352
- PROGRM to 353
- CHARS menu 354
- Using programs 355
- Transmit a 356
- Customizing an aplet 357
- Aplet naming convention 358
- Configuring the 359
- Setviews menu 359
- 21-12 Programming 360
- Programming commands 361
- Aplet commands 362
- Auto-run programs 363
- ProgramName 364
- ViewNumber 364
- Branch commands 365
- 21-18 Programming 366
- Drawing commands 367
- 21-20 Programming 368
- Graphic commands 369
- 21-22 Programming 370
- XPageNum: 370
- Loop commands 371
- Matrix commands 372
- Print commands 373
- Prompt commands 374
- Programming 21-27 375
- CMDS 376
- NOTE and type AREA IS 377
- Stat-One commands 378
- Stat-Two commands 378
- Plot-view variables 379
- Extremum 380
- Hmin/Hmax 380
- InvCross 381
- Nmin / Nmax 382
- Recenter 382
- S1mark–S5mark 382
- StatPlot 383
- Umin/Umax 383
- Tmin / Tmax 384
- Xmin / Xmax 385
- Ymin / Ymax 385
- Symbolic-view variables 386
- Numeric-view variables 388
- NumIndep 389
- NumStart 390
- StatMode 390
- Note variables 391
- Sketch variables 391
- Extending aplets 393
- 22-2 Extending aplets 394
- Resetting an aplet 395
- Sending and receiving aplets 396
- To transmit 397
- To sort the 398
- To delete an 398
- Reference information 399
- Resetting the HP 40gs 401
- Operating details 402
- To install the main 403
- To install the 403
- Variables 404
- Function aplet variables 405
- Parametric aplet variables 406
- Polar aplet variables 407
- Sequence aplet variables 408
- Solve aplet variables 409
- Statistics aplet variables 410
- MATH menu categories 411
- Physical Constants 414
- CAS functions 415
- Program commands 417
- Status messages 418
- MEMORY) 419
- Limited Warranty 421
- Regulatory Notices 425
- Korean Notice 427
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