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Manual do Utilizador
HP 48gII Graphing Calculator Manual do Utilizador Página 162
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Page 3-37
Define this function by any of the means presented above, and check that
g(-3) = 3, g(-1) = 0, g(1) = 0, g(3) = 9.
1
2
...
157
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...
863
864
Printing History
2
Preface
3
Table of contents
5
Page TOC-2
6
Page TOC-3
7
Page TOC-4
8
Page TOC-5
9
Page TOC-6
10
Chapter 9 - Vectors, 9-1
11
Page TOC-8
12
Page TOC-9
13
Page TOC-10
14
Chapter 12 - Graphics
15
Page TOC-12
16
Page TOC-13
17
Page TOC-14
18
Page TOC-15
19
Page TOC-16
20
Page TOC-17
21
Page TOC-18
22
Page TOC-19
23
Page TOC-20
24
Page TOC-21
25
Appendices
26
Page Note-1
27
Page Note-2
28
Page Note-3
29
Chapter 1
30
Getting started
30
Page 1-2
31
Page 1-3
32
Page 1-4
33
Page 1-5
34
The TOOL menu
35
Setting time and date
36
Page 1-8
37
Page 1-9
38
Page 1-10
39
Page 1-11
40
Selecting calculator modes
41
Operating Mode
42
Page 1-14
43
Page 1-15
44
Page 1-16
45
Page 1-17
46
Page 1-18
47
Page 1-19
48
Page 1-20
49
Page 1-21
50
Angle Measure
51
Coordinate System
51
)cos( yxrrx +=⋅= θ
52
Page 1-24
53
Selecting CAS settings
54
Selecting Display modes
54
Selecting the display font
55
Page 1-27
56
Page 1-28
57
Selecting the clock display
58
Chapter 2
59
Introducing the calculator
59
Page 2-2
60
Mean: 23.2, the word
61
Page 2-4
62
Page 2-5
63
Page 2-6
64
Page 2-7
65
Page 2-8
66
Page 2-9
67
Page 2-10
68
Page 2-11
69
Page 2-12
70
Page 2-13
71
Page 2-14
72
Page 2-15
73
Page 2-16
74
Page 2-17
75
Page 2-18
76
Page 2-19
77
Page 2-20
78
Page 2-21
79
Page 2-22
80
Page 2-23
81
Page 2-24
82
Page 2-25
83
Page 2-26
84
Page 2-27
85
Summations
86
Page 2-29
87
Page 2-30
88
Page 2-31
89
)cos()sin()sin(
90
Page 2-33
91
The HOME directory
92
The CASDIR sub-directory
93
Page 2-36
94
Page 2-37
95
Creating subdirectories
96
Page 2-39
97
Page 2-40
98
Page 2-41
99
Moving among subdirectories
100
Deleting subdirectories
100
Page 2-43
101
Page 2-44
102
Page 2-45
103
Variables
104
Page 2-47
105
Page 2-48
106
Page 2-49
107
Page 2-50
108
Checking variables contents
109
Page 2-52
110
Page 2-53
111
Copying variables
112
Page 2-55
113
Page 2-56
114
Page 2-57
115
Page 2-58
116
Deleting variables
117
Page 2-60
118
UNDO and CMD functions
119
Page 2-62
120
Page 2-63
121
Other flags of interest
122
CHOOSE boxes vs. Soft MENU
123
Selected CHOOSE boxes
124
Page 2-67
125
Chapter 3
126
Calculation with real numbers
126
Real number calculations
127
The inverse function
128
Using parentheses
129
Absolute value function
129
Squares and square roots
129
Powers and roots
130
Trigonometric functions
131
Page 3-7
132
Page 3-8
133
Page 3-9
134
Page 3-10
135
Real number functions
136
Page 3-12
137
Page 3-13
138
Special functions
139
)](ln[)( xx Γ=
140
Calculator constants
141
Operations with units
142
Available units
143
Page 3-19
144
Page 3-20
145
Converting to base units
146
Attaching units to numbers
147
Page 3-23
148
Page 3-24
149
Page 3-26
151
Units manipulation tools
152
Page 3-28
153
Page 3-29
154
Page 3-30
155
Special physical functions
156
Function ZFACTOR
157
Function F0λ
157
Function SIDENS
158
Function TDELTA
158
Function TINC
158
Defining and using functions
159
Page 3-35
160
Page 3-36
161
Page 3-37
162
= -1. The complex
163
. The complex
163
Entering complex numbers
164
Page 4-3
165
Page 4-4
166
The CMPLX menus
167
Page 4-6
168
Page 4-7
169
Functions from the MTH menu
170
Page 4-9
171
Chapter 5
172
Page 5-2
173
Functions in the ALG menu
174
Page 5-4
175
Page 5-5
176
Page 5-6
177
Page 5-7
178
Page 5-8
179
Page 5-9
180
INTEGER menu
181
POLYNOMIAL menu
182
MODULO menu
183
Modular arithmetic
183
Page 5-13
184
Page 5-14
185
Page 5-15
186
Page 5-16
187
Page 5-17
188
Polynomials
189
Page 5-19
190
Page 5-20
191
Page 5-21
192
Page 5-22
193
Page 5-23
194
Fractions
195
Page 5-25
196
Page 5-26
197
UNITS convert menu
198
BASE convert menu (Option 2)
199
Page 5-29
200
Page 5-30
201
Chapter 6
202
Solution to single equations
202
Function SOLVE
203
Page 6-3
204
Function SOLVEVX
205
Function ZEROS
205
Numerical solver menu
206
Polynomial Equations
207
Page 6-7
208
Page 6-8
209
Financial calculations
210
End is highlighted
211
Page 6-11
212
Page 6-13
214
1. Solve equation.. solve
215
Page 6-15
216
Page 6-16
217
Page 6-17
218
Page 6-18
219
Page 6-19
220
Page 6-20
221
Page 6-21
222
Page 6-22
223
Page 6-23
224
Page 6-24
225
Page 6-25
226
Page 6-26
227
The SOLVE soft menu
228
The SOLVR sub-menu
229
Page 6-29
230
The DIFFE sub-menu
231
The POLY sub-menu
231
The SYS sub-menu
232
The TVM sub-menu
232
Page 6-32
233
Page 6-33
234
Chapter 7
235
Solving multiple equations
235
{ ‘t = (x-x0)/(COS(θ0)*v0)’
236
Page 7-3
237
Page 7-4
238
Page 7-5
239
Page 7-6
240
Page 7-7
241
Page 7-8
242
Page 7-9
243
Page 7-10
244
Page 7-11
245
Page 7-12
246
Page 7-13
247
Page 7-14
248
Page 7-15
249
53.1301023541
250
Page 7-17
251
Page 7-18
252
Page 7-19
253
Page 7-20
254
Page 7-21
255
Chapter 8
256
Operations with lists
256
Page 8-2
257
Changing sign
258
Page 8-4
259
Page 8-5
260
Page 8-6
261
Lists of complex numbers
262
Lists of algebraic objects
263
The MTH/LIST menu
263
Page 8-9
264
List size
265
Element position in the list
266
HEAD and TAIL functions
266
The SEQ function
266
The MAP function
267
Page 8-13
268
Applications of lists
269
Harmonic mean of a list
270
Geometric mean of a list
271
Weighted average
272
Statistics of grouped data
273
Page 8-19
274
Page 8-20
275
Chapter 9
276
Entering vectors
277
Page 9-3
278
Page 9-5
280
@→STK@@ @GOTO@
280
→ keys are selected
280
Building a vector with ARRY
281
Page 9-7
282
Page 9-8
283
The MTH/VECTOR menu
285
Magnitude
286
Dot product
286
Cross product
286
Decomposing a vector
287
Changing coordinate system
288
Page 9-14
289
Page 9-15
290
Resultant of forces
291
Angle between vectors
291
Moment of a force
292
Equation of a plane in space
293
Page 9-19
294
Function LIST
295
Function ARRY
296
Function DROP
296
Page 9-22
297
Page 9-23
298
Page 9-24
299
Page 9-25
300
Chapter 10
301
Using the Matrix Writer
302
Page 10-3
303
Page 10-4
304
Page 10-5
305
Functions GET and PUT
306
Functions GETI and PUTI
306
Page 10-7
307
Function TRN
308
Function CON
308
Function IDN
309
Function RDM
310
Function RANM
311
Function SUB
311
Function REPL
312
Function →DIAG
313
Function
313
Function VANDERMONDE
314
Function HILBERT
314
Page 10-15
315
Page 10-16
316
Page 10-17
317
Function →COL
318
Function COL→
319
Function COL+
320
Function COL
320
Function CSWP
321
Function →ROW
322
Function ROW→
323
Function ROW+
324
Function ROW
324
Function RSWP
325
Function RCI
325
Function RCIJ
326
Chapter 11
327
Addition and subtraction
328
Multiplication
328
Page 11-3
329
.,,2,1;,,2,1
330
Page 11-5
331
Page 11-6
332
Function ABS
333
Function SNRM
333
Functions RNRM and CNRM
334
Function SRAD
335
Function COND
335
Function RANK
336
Function DET
337
Page 11-12
338
Page 11-13
339
Function TRAN
340
Function AXL
341
Function AXM
341
Function LCXM
341
Solution of linear systems
342
Page 11-17
343
Page 11-18
344
Page 11-19
345
Page 11-20
346
Page 11-21
347
Page 11-22
348
Page 11-23
349
Page 11-24
350
Page 11-25
351
Page 11-26
352
Page 11-27
353
Page 11-28
354
Page 11-29
355
Page 11-30
356
Page 11-31
357
Page 11-32
358
Page 11-33
359
Page 11-34
360
Page 11-35
361
Page 11-36
362
Page 11-37
363
Page 11-38
364
Page 11-39
365
Page 11-40
366
Page 11-41
367
AAUG
367
Page 11-42
368
Page 11-43
369
Eigenvalues and eigenvectors
370
Function EGVL
371
Function EGV
372
Function JORDAN
373
Function MAD
373
Matrix factorization
374
Function LU
375
Function SCHUR
376
Matrix Quadratic Forms
377
The QUADF menu
378
Page 11-53
379
Linear Applications
380
Function KER
381
Function MKISOM
381
Chapter 12
382
Graphics
382
Page 12-2
383
Page 12-3
384
Page 12-4
385
Page 12-5
386
Page 12-6
387
Page 12-7
388
Page 12-8
389
. Type LN(X). Press ` to
390
Page 12-10
391
The PPAR variable
392
Page 12-12
393
Page 12-13
394
Page 12-14
395
Page 12-15
396
Page 12-16
397
Page 12-17
398
The TPAR variable
399
Plots in polar coordinates
400
Page 12-20
401
Plotting conic curves
402
Page 12-22
403
Parametric plots
404
Page 12-24
405
Page 12-25
406
Page 12-26
407
Page 12-27
408
Page 12-28
409
Truth plots
410
Bar plots
411
TYPE to Bar
412
V-View: 0 5
412
Scatter plots
413
H-View: 0 6, V-View: 0 6
414
H-View: 0 7, V-View: 0 7
414
Slope fields
415
Fast 3D plots
416
Page 12-36
417
Wireframe plots
418
Page 12-38
419
Ps-Contour plots
420
TYPE to Ps-Contour
421
Y-Slice plots
422
Gridmap plots
423
Pr-Surface plots
424
Interactive drawing
425
DOT+ and DOT
426
Page 12-46
427
Page 12-47
428
Page 12-48
429
ZFACT, ZIN, ZOUT, and ZLAST
430
ZDFLT, ZAUTO
431
HZIN, HZOUT, VZIN and VZOUT
431
The SYMBOLIC menu and graphs
432
The SYMB/GRAPH menu
433
Page 12-53
434
Function DRAW3DMATRIX
435
Chapter 13
436
Calculus Applications
436
)(lim xf
437
The DERIV&INTEG menu
438
Page 13-4
439
Page 13-5
440
The chain rule
441
Derivatives of equations
441
Application of derivatives
442
Page 13-8
443
Function DOMAIN
444
Function TABVAL
444
Function SIGNTAB
445
Function TABVAR
445
Page 13-11
446
Page 13-12
447
Higher order derivatives
448
CxFdxxf +=
449
),()()( aFbFdxxf
450
Page 13-16
451
Page 13-17
452
Integrating an equation
453
Techniques of integration
453
−= vduuvdudv )( . Since by
454
−= vduuvudv
454
Page 13-20
455
Integration with units
456
Page 13-22
457
Infinite series
458
).()()( xRxPxf
459
Page 13-26
461
Chapter 14
462
Page 14-2
463
Higher-order derivatives
464
⋅(∂z/∂y) + (dx/dt)⋅(∂z/∂x)
465
(∂z/∂x)⋅dx + (∂z/∂y)⋅dy
466
Page 14-6
467
Page 14-7
468
Multiple integrals
469
470
Page 14-10
471
[] [] [] []
472
Page 15-2
473
Potential of a gradient
474
Divergence
475
Laplacian
475
[] [] []
476
Vector potential
477
Page 15-7
478
Chapter 16
479
Differential Equations
479
Page 16-2
480
Page 16-3
481
The CALC/DIFF menu
482
Function LDEC
483
Page 16-6
484
Function DESOLVE
485
.)3/exp(5)3/exp()(
486
Exact expressions, ‘y(0)
487
Laplace Transforms
488
.)()())(*(
489
Laplace transform theorems
490
Page 16-13
491
)})(*{()()(
492
=− ).()()(
493
= .0.1)( dxxδ
493
Page 16-16
494
Delta(5)’
495
Page 16-18
496
Page 16-19
497
Page 16-20
498
Page 16-21
499
)3()3sin(sincos)(
500
−⋅−+⋅+⋅= tHttCtCoty
500
Indep is set to ‘X’
501
.)3(sinsincos)(
503
⋅⋅−⋅+⋅+⋅= dueuHttCtCoty
503
Page 16-26
504
Fourier series
505
Function FOURIER
506
Page 16-29
507
Page 16-30
508
Page 16-31
509
+= 0)0,,( cckXF
510
Page 16-33
511
Page 16-34
512
Page 16-35
513
Page 16-36
514
Page 16-37
515
Page 16-38
516
Page 16-39
517
Page 16-40
518
Page 16-41
519
Page 16-42
520
Fourier Transforms
521
Page 16-44
522
Page 16-45
523
Fourier sine transform
524
Page 16-47
525
Page 16-48
526
Page 16-49
527
Examples of FFT applications
528
Page 16-51
529
Page 16-52
530
=+⋅−+ bnan
531
Legendre’s equation
532
Bessel’s equation
533
Page 16-56
534
⋅x), where i is
535
Laguerre’s equation
536
Page 16-59
537
Page 16-60
538
Page 16-61
539
Page 16-62
540
Page 16-63
541
Page 16-64
542
Page 16-65
543
Page 16-66
544
Page 16-67
545
Page 16-68
546
Page 16-69
547
Function RKF
548
Function RRK
549
Function RKFSTEP
550
Function RRKSTEP
551
Function RKFERR
552
Function RSBERR
552
Page 16-75
553
Chapter 17
554
Probability Applications
554
Random numbers
555
Page 17-3
556
Binomial distribution
557
Poisson distribution
558
The gamma distribution
559
The exponential distribution
560
The beta distribution
560
The Weibull distribution
560
Page 17-8
561
Normal distribution pdf
562
Normal distribution cdf
563
The Student-t distribution
564
The Chi-square distribution
564
The F distribution
565
Page 17-13
566
Page 17-14
567
Page 17-15
568
Page 17-16
569
Page 17-17
570
Page 17-18
571
Chapter 18
572
Statistical Applications
572
Sample
573
Page 18-3
574
Median: 2.15
575
Type: Population in the
576
Page 18-6
577
Page 18-7
578
Page 18-8
579
Page 18-9
580
Page 18-10
581
Page 18-11
582
Page 18-12
583
Calculation of percentiles
585
The STAT soft menu
586
The ΣPAR sub-menu
587
The 1VAR sub menu
587
The PLOT sub-menu
588
The FIT sub-menu
589
The SUMS sub-menu
589
Page 18-19
590
'1.5+2*X'
591
Intercept: 1.5, Slope: 2
591
Page 18-21
592
Confidence intervals
593
Definitions
594
Page 18-24
595
Page 18-25
596
Page 18-26
597
Page 18-27
598
Page 18-28
599
Page 18-29
600
Page 18-30
601
Page 18-31
602
Page 18-32
603
Page 18-33
604
Hypothesis testing
605
Errors in hypothesis testing
606
Page 18-36
607
Page 18-37
608
Page 18-38
609
Page 18-39
610
Paired sample tests
611
Page 18-41
612
Page 18-42
613
Page 18-43
614
Page 18-44
615
Page 18-45
616
Page 18-46
617
Page 18-47
618
Page 18-48
619
The method of least squares
620
Page 18-50
621
Prediction error
622
Page 18-52
623
P-value < α
624
5.2427905694150.0)15()1(
625
Page 18-55
626
Multiple linear fitting
627
Page 18-57
628
Polynomial fitting
629
Page 18-59
630
Page 18-60
631
Page 18-61
632
Selecting the best fitting
633
Page 18-63
634
Page 18-64
635
Chapter 19
636
Numbers in Different Bases
636
Page 19-2
637
Page 19-3
638
! is
638
Wordsize
639
The LOGIC menu
640
The BIT menu
641
The BYTE menu
641
Page 19-7
642
Chapter 20
643
Page 20-2
644
Page 20-3
645
Page 20-4
646
Customizing the keyboard
647
Operating user-defined keys
648
Page 20-7
649
Chapter 21
650
[']~„gK
651
Page 21-3
652
Global Variable Scope
653
The PRG menu
654
Functions listed by sub-menu
655
Page 21-7
656
Page 21-8
657
Shortcuts in the PRG menu
658
Page 21-10
659
Page 21-11
660
Page 21-13
662
},...,,,{
663
Page 21-15
664
Page 21-16
665
Page 21-17
666
* SQ * 2 * SWAP SQ SWAP / »
667
Page 21-19
668
⋅⋅⋅ SSSQS
669
Prompt with an input string
670
:a:35 in stack level 1
671
INPUT OBJ→ → a
671
‘2*a^2+3‘ » »
671
‘2*a^2+3’ » which uses the
672
<!> Interrupted
672
Page 21-24
673
« ‘2*a^2+3‘ NUM » »
673
V T ‘(1.662902_J/K)*(T/V)’ »
674
Page 21-26
675
Input through input forms
676
Page 21-28
677
Page 21-29
678
MSGBOX END »
679
Creating a choose box
680
Page 21-32
681
Tagging a numerical result
682
Examples of tagged output
683
Using a message box
686
Page 21-38
687
« V T n
687
Page 21-39
688
STR ‚Õ ‚ë ™+
688
Page 21-40
689
Page 21-41
690
« », and some steps
690
Page 21-42
691
Relational operators
692
Logical operators
693
Page 21-45
694
Branching with IF
695
Page 21-47
696
Page 21-48
697
Page 21-49
698
Page 21-50
699
The CASE construct
700
Page 21-52
701
Program loops
702
Page 21-54
703
Page 21-55
704
« - start subprogram)
704
Page 21-56
705
Page 21-57
706
Page 21-58
707
The FOR construct
708
1 0 START 1 1 STEP
709
The DO construct
710
The WHILE construct
711
Page 21-63
712
Errors and error trapping
713
LASTARG
714
Sub-menu IFERR
714
Page 21-66
715
« → X ‘2.5-3*X^2’ »
715
Page 21-67
716
Chapter 22
717
Page 22-2
718
Page 22-3
719
Page 22-4
720
Page 22-5
721
Page 22-6
722
Page 22-7
723
Page 22-8
724
Page 22-9
725
Page 22-10
726
Page 22-11
727
Page 22-12
728
Page 22-13
729
Two-dimensional graphics
730
Three-dimensional graphics
731
The variable EQ
731
Page 22-16
732
Page 22-17
733
Page 22-18
734
Page 22-19
735
Page 22-20
736
Page 22-21
737
PIX?, PIXON, and PIXOFF
738
Page 22-23
739
Page 22-24
740
Pixel coordinates
741
Animating graphics
742
Page 22-27
743
Page 22-28
744
LIST ³ ~~wlist~ K
744
Page 22-29
745
Graphic objects (GROBs)
746
The GROB menu
747
Page 22-32
748
Page 22-33
749
Page 22-34
750
Page 22-35
751
Modular programming
752
Running the program
752
Page 22-37
753
{ 25 75 50 } [ENTER]
754
Page 22-39
755
Page 22-40
756
Page 22-41
757
Chapter 23
758
Character strings
758
String concatenation
759
The CHARS menu
759
The characters list
760
Page 23-4
761
S, or ~‚s. Some
761
Chapter 24
762
Calculator objects and flags
762
Page 24-2
763
Calculator flags
764
User flags
765
Chapter 25
766
Date and Time Functions
766
Browsing alarms
767
Calculations with dates
768
Calculating with times
769
Alarm functions
769
Chapter 26
770
Managing memory
770
Checking objects in memory
771
Backup objects
772
Page 26-4
773
Using data in backup objects
774
Using libraries
775
Backup battery
776
Page 26-8
777
Appendix A
778
Using input forms
778
Page A-2
779
Page A-3
780
Page A-4
781
Appendix B
782
The calculator’s keyboard
782
Page B-2
783
Main key functions
784
Alternate key functions
785
Left-shift functions
786
Page B-6
787
Page B-7
788
Right-shift functions
789
ALPHA characters
790
Alpha-left-shift characters
791
Page B-11
792
" '
793
Page B-13
794
Appendix C
795
CAS settings
795
Page C-2
796
Selecting the modulus
797
Page C-4
798
Page C-5
799
Complex vs. Real CAS mode
800
Step-by-step CAS mode
801
Page C-8
802
Increasing-power CAS mode
803
Rigorous CAS setting
803
Using the CAS HELP facility
804
Page C-11
805
Page C-12
806
Page C-13
807
Page C-14
808
Appendix D
809
Additional character set
809
Page D-2
810
Greek letters
811
Other characters
811
Appendix E
812
Page E-2
813
Page E-3
814
Page E-4
815
Appendix F
816
The Applications (APPS) menu
816
I/O functions
817
Constants lib
817
Numeric solver
818
Time & date
818
Equation writer
818
File manager
819
Matrix Writer
819
Text editor
820
Math menu
820
CAS menu
821
Appendix G
822
Useful shortcuts
822
Page G-2
823
Page G-3
824
Appendix H
825
The CAS help facility
825
Page H-2
826
Appendix I
827
Command catalog list
827
Appendix J
828
The MATHS menu
828
The HYPERBOLIC sub-menu
829
The INTEGER sub-menu
829
The MODULAR sub-menu
829
The POLYNOMIAL sub-menu
830
The TESTS sub-menu
830
Appendix K
831
The MAIN menu
831
The MATHS sub-menu
832
The ARIT sub-menu
833
The EXP&LN sub-menu
834
The MATR sub-menu
834
Page K-5
835
Appendix L
836
Line editor commands
836
Page L-2
837
The SEARCH sub-menu
838
The GOTO sub-menu
838
The Style sub-menu
839
840
Appendix M
841
Page M-2
842
Page M-3
843
Page M-4
844
Page M-5
845
Page M-6
846
Page M-7
847
Page M-8
848
Page M-9
849
Page M-10
850
Page M-11
851
Page M-12
852
Page M-13
853
Page M-14
854
Page M-15
855
Page M-16
856
Page M-17
857
Page M-18
858
Page M-20
860
Limited Warranty
861
Service
862
Page W-3
863
Regulatory information
864
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