Hp 48g Graphing Calculator Manual do Utilizador Página 242
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INTEGRATE j
EKPR:
VAR: LQ:
RESULT: Humeric
NUMBER FURMAT: Std
ENTER EKPRESSI0N
The Numeric INTEGRATE Screen.
20
(5. Set the number display format to indicate the accuracy factor you
desire for the computation. The Std format yields the highest
accuracy factor (and consequently the longest calculation time)
while Fix 0 (or Sci 0 or Eng 0) yields the lowest accuracy factor
(and the shortest calculation time). See “The Accuracy Factor and
the Uncertainty of Numerical Jntegration” on page 20'^6.
7. Press OK to compute the integral.
Improper integrals are those integrals where one or both limits are
infinity (oc). The HP 48 is a calculator with finite computational
limits and thus must always use finite limits when computing numeric
integrals. However, b}' using a transformation of variables, jmu can
map an unbounded domain onto a bounded one.
One useful transformation, y = arctan x, maps the entire real ,r-axis
onto the bounded interval ^ < y < f ■ This is the transformation:
f(x)dx
ar eta 7100= ^
a7'ctan—co= -
/(tan ij) • (1 + tan ''y)dy
To evaluate an improper integral:
1. Make sure that you are in Radian mode (press RAD), if
necessary).
2. Press fr^fSYMBOLIC 1 OK to open the ! form.
3. Enter the integrand from tl«' improper integral into the ExF'FOi
field.
4. With the Ex
field highlighted, press f NXT ) CFlLC and enter
the transformation expression onto the stack. For example, if the
variable of integration for the improper integral is x. you would
enter TflNCf) to make the transformation {x = tany) shown
above. Make a extra copy of transformation expression by pressing
(enter) a second time.
20-2 Calculus and Symbolic Manipulation
- HP 48G Series 1
- Regulatory Information 2
- WKSl HEWLETT 3
- HP Part No. 00048-90126 3
- Printed in Singapore 3
- Acknowledgements 4
- Edition History 4
- Contents 5
- Stack Command Menu 6
- 7. The Equation Writer 7
- Contents-4 8
- Contents-5 9
- Contents-6 10
- Contents-7 11
- Contents-8 12
- Contents-9 13
- Contents-10 14
- Organization of the Display 15
- {(.)> 16
- The Stack 17
- Organization of the Keyboard 18
- ^ ! j ■ 19
- To cancel a shift key: 20
- Cursor Keys 21
- Menus: Extending the Keyboard 22
- , Г. . . . . . . . . . j г 23
- To display the previous menu: 24
- To key in a simple number: 25
- 123.4 i 26
- To key in a single character: 27
- Keying in Special Characters 28
- 'abcdefghijkImno 29
- [SPC) between each element 30
- Using the Command Line 31
- Command Line Operations 32
- !r»i I ENTRY 33
- Viewing and Editing Objects 34
- Viewing or Editing an Object 35
- 2 Using the EDIT Menu 36
- EDIT Menu Operations 36
- №liEDIT ]: 36
- O ■ ^■ C'EL 36
- Making Calculations 37
- 3.7 (a(LN) 38
- 2401 fsp^ 4 39
- 3-4 Stack 40
- To clear the entire stack: 41
- The Interactive Stack 42
- Interactive-Stack Operations 43
- C' R P N 44
- 8mn3HamiS8a«iajiiaiinM3EMi5i 46
- Cormiiand/Description 47
- Input Output 47
- DEPTH Returns the 47
- DUPN Duplicates n 47
- 3-12 Stack 48
- Using the MODES Application 49
- Setting the Display Mode 50
- Mode Definition Annunciator 51
- 4-4 Modes 52
- [rzGzct)] 53
- Modes 4-5 53
- 4 Setting the Beep 54
- 1. Press 54
- Setting the Clock Display 54
- Setting the Fraction Mark 54
- To set the fraction mark: 55
- To use a flag command: 56
- MODES Submenus 57
- MODES Operations 58
- Memory 5-1 59
- PICT) and the 60
- Memory 5-3 61
- Where to Store Variables 62
- ^^neJECTS IN i HBHE } 63
- Creating New Variables 63
- 5-6 Memory 64
- (MEMORY) 65
- To edit a variable: 66
- 67
- (CANCEL)) 67
- To move a variable: 68
- To purge variables: 68
- Using Variables; The VAR Menu 69
- (33 0PT I 0 (ENTER) 70
- Defining Variables 71
- Evaluating Variables 71
- '1: 72
- 'fl+B' 72
- : 'RDD£' 73
- 5 Special Memory Operations 74
- Memory Reset 75
- Memory Reset Prompt 76
- Memory 5-19 77
- 5-20 Memory 78
- InpRiit Foniìs and Lists 79
- (ENTER) or 81
- ENTER ) or 81
- [ENTER) or OK 82
- (ENTER) or UK 83
- « Program »■ 84
- Real number L 84
- EQ) and system flags are 85
- (ENTER) (3(iD (SCZD 86
- (ENTER) (3I2D 1 fS^ 5 86
- (enter) (3(Tg (ENTER) Q© 86
- SFIRST ONES 86
- U=M0+ adtD 87
- Organized 88
- Constructing Equations 89
- To include exponents: 90
- To include roots: 90
- To include powers of 10: 91
- To include units: 92
- E) 2(3X0 2(3 93
- 0 1 0(0X 93
- ©X(03E2 0X020 93
- 2 ©X @©Y (cos) 94
- (ZD 2 ©® 95
- 0 © 1 © 95
- To edit by backspacing: 96
- To edit the full equation: 96
- @0 0 ©) 10 (© 97
- 5. Press REF1... 98
- 7-12 The EquationWriter 98
- Description 100
- (i±JLi_D 100
- The HatrixWriter 101
- Entering Arrays 102
- [[ 2 -£ 0 ] 103
- 8-4 The MatrixWriter 104
- Editing Arrays 105
- To insert a column: 106
- To delete a column: 107
- To insert a row: 107
- To delete a row: 107
- 8-8 The MatrixWriter 108
- Graphic Objects 109
- The PICTURE Environment 110
- Using the Picture Editor 110
- Graphic Objects 9-3 111
- 9-4 Graphic Objects 112
- 113
- FTliCLEARl E 113
- 9-6 Graphic Objects 114
- Graphic Object Coordinates 115
- Graphic Object Commands 116
- Graphic Objects 9-9 117
- Key P r ogr ammable 118
- Unit Objects 119
- The UNITS Catalog Menu 120
- Creating a Unit Object 121
- ® S) HQ© O 6 @ F 122
- Converting Units 123
- To convert to any units: 124
- Calculating with Units 125
- 1: 703. l£5_ft''2/d 126
- 1: 8_ft^3^s''3 127
- Percentage 127
- 1 ^ ' 128
- 1 BHMBEMBBaHBB 128
- 25_“C/nin 129
- £5_TFmin 129
- 45_°FFpiin 129
- 10 @(U1I1D(EHD 130
- UNITS) mh; 131
- Unit Objects 10-13 131
- Creating User-Defined Units 132
- H is treated as a prefix 134
- Symbolic Constants 136
- S)( -»NUMf 137
- User-Defined Functions 138
- CD© z 3(PUM3 140
- © © 3 X dED 3 Y (spc) 141
- 9 (ENTER)18(ENTER)21 142
- (VAR) BOXR 142
- 1: .4285?1428571 142
- Functions of Real 143
- Complex 143
- Trigonometric Functions 144
- Hyperbolic Functions 145
- Probability Commands 146
- Test Statistics Commands 147
- (IvrnTl fN^ 148
- Real Number Functions 149
- Percent Functions 151
- Other Real-Number Functions 151
- Complex Numbers 153
- S)0> enter the 154
- Other Complex-Number Commands 155
- ¥eet®cs and 157
- [rz:eztt)] 158
- Entering 2D and 3D Vectors 159
- Vector Math Commands 160
- Vectors and Transforms 13-5 161
- 1: [ 178.937160532 162
- ¿111.148894255 ] 162
- 1: 78.8585649505 162
- Fast Fourier Transforms 163
- 13-8 Vectors and Transforms 164
- 6. Press (ENTER) 166
- Disassembling Matrices 168
- Inserting Rows and Columns 169
- Extracting Rows and Columns 170
- Swapping Rows and Columns 170
- Characterizing Matrices 171
- Transforming Matrices 174
- (AB) of two matrices: 175
- Expressions 176
- OdD ©O J S30 ® o 177
- Transforming Complex Matrices 177
- Equations 178
- Operations 182
- H T R R 0 W R S W P 183
- MODES) FLFiG 54 184
- To recoiTstruct ; 186
- Binary Integers and Bases 187
- (MTH ) BFlSE fNXT) RC 188
- To enter a binary integer: 188
- (ENTER 1 188
- ED or 0 189
- Using Boolean Operators 190
- Manipulating Bits and Bytes 190
- 1 “ ^ H0iB£lC6h 191
- Calculating with Dates 193
- 1: 4.301993 194
- 1= 1565 194
- Calculating with Times 195
- T I CKS to start timing 196
- Calculating with Fractions 197
- ______________ 198
- ' 987-^1 £5' 198
- Lists and Sequences 199
- List Processing 200
- SKU) 3 fSPC) 4 fspci 5 200
- { 4 5 6 } 201
- { 4 10 20 }I 201
- 17-4 Lists and Sequences 202
- SKU) 1 dED 2 dED 3 dED 203
- List Manipulations 204
- Sequences 205
- 6. Execute SEQ 206
- Solving Equations 207
- ENTER FUNCTION TD_ SOLVE 208
- To interpret the comput ilt: 209
- 18-4 Solving Equations 210
- Solving Options 211
- 18-6 Solving Equations 212
- To enter jriiTient: 213
- ST (enter) 214
- (^^[SOLVEI 215
- To use the polynomial roc 216
- ■ finder: 216
- To find all roots ilynomial: 216
- 1. Press iT^fSOCTEl (A) ® U 217
- (enter) to duplicate it 218
- STACK) F 218
- SOLVE) :E 218
- Using the Finance Solver 219
- 1 ^ 2 I 3 4 ^ 5 ^ 220
- ^ 2 ^ 3 4 5 y 221
- 18-16 Solving Equations 222
- (EHD® ® 223
- PYR = 12; End mode 224
- 0.00 End 225
- To calculate amortization: 225
- 18-20 Solving Equations 226
- Differential Equations 227
- ¿final 228
- 19-2 Differential Equations 228
- Differential Equations 19-3 229
- —1000 *{y — sin{t)) + cos{t) 230
- T (ENTER) 231
- (^ (ENTER) 231
- (ENTER) 231
- (ENTER)1 (ENTER) 231
- OUDSKID 0 dED 1 232
- ^^*PLDT V'CTJ:Fa,V)^^M 233
- TOiaHOTHKiiiaitiBiligamBi 233
- 19-8 Differential Equations 234
- (0 2 (ENTER) 235
- 19-10 Differential Equations 236
- 0 (IE) © T (ENTER) (0 237
- Qcm acm 238
- SIGD •5®©te)i 239
- Integration 241
- The Numeric INTEGRATE Screen 242
- RAD), if 242
- H^iSYMBOLICl OK 243
- 1: .693147180555 244
- T-cos(e) 245
- Symbolic integration 247
- Symbolic 248
- Differentiation 249
- Y and dZ<Y> 251
- Implicit Differentiation 252
- TAYLOR POLYNOMIAL I 253
- The TAYLOR POLYNOMIAL Screen 253
- OK to open the ISOLATE H 255
- Press MODES) FLAG 256
- Showing Hidden Variables 257
- (»^fSYIVIBOLIC) 258
- Manipulating Subexpressions 259
- EQUATION) and key it in 259
- PICTURE IRI 259
- (ENTER 1, or fCANCEL) 260
- (ENTER) to see the new 261
- Distributing 263
- Distributing (continued) 264
- KB, and Kn-arie 268
- 'SIN(2*(X+n> 269
- Symbolic Integration Patterns 270
- Antiderivative 271
- Statistic^ Dñcí 273
- 275
- Editing Statistical Data 276
- ) MFiTR CuL COL..+ 277
- = 31n.c — 4 278
- Generating Frequencies 280
- /ariabis; 282
- _2Ke_EYS _EKV _NE 283
- Plotting 285
- INDEP: X H-VIEW:-6.5 6.5 286
- _flUTDSCflLE V-VIEW;-3.1 3.2 286
- ENTER FUMCTIDNtS), TO PLDT 286
- __________ 286
- The Default PLOT Screen 286
- EQs field 287
- EQ” by pressing OK 287
- 22-4 Plotting 288
- Environment 289
- Using Zoom Operations 290
- Setting Zoom Defaults 291
- Selecting a Zoom 291
- 22-8 Plotting 292
- Analyzing Functions 293
- The PICTURE FCN Menu 294
- Plotting 22-11 295
- 22-12 Plotting 296
- Plotting 22-13 297
- Contents of the PPAR List 298
- Description Default 299
- 22-16 Plotting 300
- Plot Types 301
- The Function PLOT Form 301
- 23-2 Plot Types 302
- TRACE Mode 303
- Special Notes 303
- Polar Plots 304
- The Parametric PLOT Form 307
- Examples 309
- 1 = 6.5 or do their 309
- 23-10 Plot Types 310
- Differential Equation Plots 311
- Conic Plots 311
- The Conic PLOT Form 312
- The Conic PLOT OPTIONS Form 312
- EXAMPLES directory then: 313
- Truth Plots 314
- (aCELHD®@c 316
- Statistical Plots 317
- Histogram Plots 318
- Bar Plots 319
- Scatter Plots 320
- The Scatter PLOT Form 321
- The Scatter PLOT OPTIONS Form 321
- Sampling Grid 322
- Output Grid 322
- Slopefield/Ps-Contour 323
- The YSLICE View 324
- Slopefield Plots 325
- The Slopefield PLOT Form 326
- 8 steps 327
- 1 of the stack 327
- Wireframe Plots 328
- The Wireframe PLOT Form 329
- Pseudo-Contour Plots 330
- The Ps-Contour PLOT Form 331
- Y-Slice Plots 332
- The YSlice PLOT OPTIONS Form 333
- The Gridmap PLOT Form 334
- Parametric Surface Plots 335
- The Pr-Surface PLOT Form 336
- F" T II 337
- Press fVAR) EkFIM 338
- NXT) LHBEL. The names 339
- 24-2 Advanced Plot Options 340
- [PRG) FGCT F'DIM 341
- 24-4 Advanced Plot Options 342
- (PRG) P I C T P D I M 343
- Saving and Restoring Plots 344
- Advanced Plot Options 24-7 345
- SKMDSI E0 to restore EQ 346
- HP 48G Series Advanced 347
- User’s Reference 347
- Using the Solver 348
- Using the Menu Keys 349
- Actions for Solver Menu Keys 349
- Q _ rO rr I 350
- Viewing the Picture 351
- Operation Key 352
- S) Pil-L 353
- O H1- !-■ 353
- Defining a Set of Equations 354
- Xi = Vo + a ■ ti 355
- {X2 - xi) = a ■ {to - h) 355
- Checking Solutions 356
- The Equation Library 25-11 357
- Using the Constants Library 358
- 02 dielectric constant 3.9 359
- Minehunt Game 360
- User-Defined Units 361
- 1. Press f7» 363
- To change the date or time; 364
- To set an appointment alarm: 365
- 1 enter 15 365
- Responding to Alarms 366
- Viewing and Editing Alarms 367
- Pj^fMODESl F'LFlG CF 368
- MODES 1 FLFiG 368
- Printing 370
- To set up a serial printer: 371
- I DEJECT; 372
- The Wire PRINT Screen 373
- PRINT PRST 374
- Computer 375
- The Wire TRANSFER Screen 376
- Using Kermit 377
- CHCujS OK to browse the 378
- TRANSFER form 378
- I-- I N 1 H 378
- Choosing and Using File Names 379
- Backing Up HP 48 Memory 380
- Sending Kermit Commands 381
- Using XMODEM 382
- Using Other Serial Protocols 383
- Ports and Piiyg-^n Cards 389
- Card Slot 1 390
- Card Slot 2 390
- Using Backup Objects 391
- To ewaluate a tjackyp object: 392
- To delete a backup object: 392
- Backing Up All Memory 393
- Using Libraries 394
- Write contents 399
- Read-only setting 400
- To remove a plug-in card: 402
- LIBRARY) 403
- LIBRARY) MERG . If 404
- ProgicaimiiitcRij the iiiP 407
- The Contents of a Program 408
- Programming the HP 48 29-3 409
- Calculations in a Program 410
- Structured Programming 410
- To enter a program: 411
- CD (©(hold) VOL (release) 413
- 1- 268.082573106 414
- Programming the HP 48 29-9 415
- Using Programming Structures 416
- CASE...END 417
- Loop Structures 418
- STF loop-clause NEKl 418
- STEP ... s 418
- S) FOF:; . Its syntax is 419
- DO...UNTIL...END 420
- WHILE...REPEAT...END 420
- Error Trapping Structures 421
- Using Local Variables 422
- Evaluating Local Names 423
- ■tiefining procedure: 424
- Directory 425
- HP 48G/GX 426
- Programming the HP 48 29-21 427
- Customizing Menus 429
- “MOLUtlE" CST } 430
- 1: .001075_m"3 430
- .0010?5_P1'"3 430
- 1: "VOLUME" 430
- ^THG l! MOLUME: .0010?5_r^3 431
- "MOLUME" CST } 431
- Customizing the Keyboard 432
- To actiwate User mode: 433
- KEYS STUK 434
- Disabling User Keys 435
- KEYS RCLK 0 DELK ST OK 436
- Answers to Common Questions 437
- Q: What does “object” mean? 438
- Environmental Limits 440
- When to Replace Batteries 440
- Changing Batteries 441
- 1 to turn the calculator on 443
- Nail grip 444
- Testing Calculator Operation 445
- Self-Test 446
- Keyboard Test 447
- Port RAM Test 448
- IR Loop-Back Test 449
- Serial Loop-Back Test 450
- Limited One-Year Warranty 451
- ■rrop Messages 455
- Sicursio^ 456
- .1 i i t- Г Г U j-‘ !.• e и 457
- (ENTER), or STR^ due 458
- ri-B i G JiU D -B X- •“! 459
- 0 g 01. i I..! 0 459
- Message Meaning 461
- V e B u f f e r 462
- Error Messages B-9 463
- B-10 Error Messages 464
- Menus C-1 465
- System Flags 467
- System Flags (continued) 468
- D-2 System Flags 468
- System Flags D-3 469
- D-4 System Flags 470
- System Flags D-5 471
- D-6 System Flags 472
- Table of Units E-1 473
- HP 48 Units (continued) 474
- E-2 Table of Units 474
- Table of Units E-3 475
- St (Stere) 476
- Table of Byilt-ln Equations 477
- Energy (31,36) 478
- Operatic"r h 481
- 1 Solve finance... HPiUK 482
- Operation Index G-3 483
- (x) containing 484
- Operation Index G-5 485
- G-6 Operation Index 486
- 1 EDIT CIRCL 487
- G-8 Operation Index 488
- ) MFiTR MflKE CON 489
- G-10 Operation Index 490
- Operation Index G-11 491
- G-12 Operation Index 492
- Operation Index G-13 493
- G-14 Operation Index 494
- Operation Index G-15 495
- G-16 Operation Index 496
- Operation Index G-17 497
- G-18 Operation Index 498
- Operation Index G-19 499
- G-20 Operation Index 500
- 1 (NXTI CM PL IM 501
- 1 (NXT 1 3 D V P H R 501
- G-22 Operation Index 502
- Operation Index G-23 503
- ] 1- I 1 ¿1.1 N E 504
- 3 R U R R S U 505
- 3 RULES n 505
- 3 R U ^ R R 3 n 505
- Operation index G-27 507
- G-28 Operation Index 508
- Operation Index G-31 511
- 2/) of a given type 512
- 1 PK I N \ KkTKM PK I pH 513
- 1 fNXT ) PURG 514
- 1 H V HI K b 514
- Operation Index G-35 515
- FLfiG ÍNXT) RCLF 516
- DfiTfl SDFiT 516
- PROB RDZ 516
- G-36 Operation Index 516
- PPliR RE.S 517
- 3D fNXTl 517
- VpfIR iNXT) RESET 517
- Operation Index G-37 517
- SOLVE) D I FFE Rl<FE 518
- D I F F E K RF i 518
- G-38 Operation Index 518
- BASE (NXT) BIT RR 519
- Operation Index G-39 519
- 2), a possible step 520
- PROC iNXT) SEQ 522
- I T H fNXT) S I H V 522
- G-42 Operation Index 522
- C; j fj p p' 523
- NLIKM oNKh 523
- 1 BfiSE fNXT) E:IT SR 524
- 1 FMT STD 524
- G-46 Operation Index 526
- Operation Index G-47 527
- r u t h 529
- Operation Index G-49 529
- PROB fNXin UTPF 531
- PROB (NXTl UTPN 531
- Operation Index G-51 531
- L- ri N M i i„ E w H j. L. t 532
- Operation Index G-53 533
- Operation Index G-55 535
- G-56 Operation Index 536
- Operation Index G-57 537
- G-58 Operation Index 538
- Commands 539
- ^checksum 541
- •’^XCOl •^ycol “ 542
- •^correlation 542
- •^covariance 542
- ■ ’^^Darcy 542
- >^n ew 543
- '’index 543
- { -i^start -^end } 543
- ■ ^sta rt 543
- ■ ^e n d 543
- 'symb' Xy 545
- 'symb' —^ 545
- 'symb' 546
- ,symb2)' 546
- ^increment 547
- { global } 548
- ' 0/1 550
- "ALL" ^ 551
- ‘name‘ ^ X 552
- "message" 552
- " string.^" 553
- 'NOT symb' 553
- for the first character 553
- [[^11 ■ ■ ■ n ]] Xll 554
- "prompt" 557
- X_ un/tj^ 558
- \epeat > 559
- •^m e n u 559
- 2 [[ matrix ]]3 560
- { list } 561
- { guesses } 561
- ■X LvI 4 LvI 3 562
- ■ ’^sdevl 563
- ■ ^sdev2 ■ ■ ■ ^sdevm ] 563
- ■ ’^density 563
- 'symb^ ' 567
- 'symb2 ' 567
- { global 568
- TVM variable' 568
- Object Type Numbers 568
- 'name' 569
- ■^port ■ 569
- Xfactor 569
- 'name' —► 571
- •’‘’left •’‘right 572
- 'ZFACTOR(sym£)j^ .symb^Y 573
- •’‘'low 574
- ■ ’‘’high 574
- 2 ' 575
- ^ Level 1 576
- 1 ... X]^ 1 ■ • m ]] 577
- Special characters 579
- L J for matrices, 2-6, 8-1 586
- Index-10 588
- Index-11 589
- Index-12 590
- Index-13 591
- Index-15 593
- Index-16 594
- Index-17 595
- Index-18 596
- Index-19 597
- Index-20 598
- Index-21 599
- Index-22 600
- PRG annunciator, 1-3, 29-5 601
- RiZ annunciator, 12-11, 13-2 602
- Index-24 602
- Index-25 603
- Index-26 604
- Index-27 605
- Index-28 606
- Index-29 607
- 10-2, 10-6 608
- Index-31 609
- Index-32 610
- Contacting Hewlett-Packard 611
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