Hp 32SII Manual do Utilizador Página 328
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C–14 More about Solving
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
Solve for X using initial guesses of 10
–8
and –10
–8
.
Keys: Display: Description:
`
8
_
H
X
1
_
`
8
_
..
_
Enters guesses.
{
V
J
.).
Selects program "J" as the
function.
{
X
!
No root found using very small
guesses near zero (thereby
restricting the search to the flat
region of the function).
@
9
9
).
)
)
The last two estimates are far
apart, and the final value of f(x) is
large.
If you use larger guesses, then SOLVE can find the roots, which are outside
the flat region (at x = 2 and x = –2).
Round–Off Error
The limited (12–digit) precision of the calculator can cause errors due to
rounding off, which adversely affect the iterative solutions of SOLVE and
integration. For example,
0 10 - ]10 1) x [(
30215
=++
has no roots because f(x) is always greater than zero. However, given initial
guesses of 1 and 2, SOLVE returns the answer 1.0000 due to round–off
error.
Round–off error can also cause SOLVE to fail to find a root. The equation
0 7-x
2
=
has a root at
7
. However, no 12–digit number exactly equals
7
, so
the calculator can never make the function equal to zero. Furthermore, the
- HP 32SII 1
- RPN Scientific Calculator 1
- Owner’s Manual 1
- Printing History 2
- Contents 3
- 4. Real–Number Functions 5
- 5. Fractions 6
- 8. Integrating Equations 7
- 11. Statistical Operations 8
- Part 2. Programming 9
- 12. Simple Programming 9
- 13. Programming Techniques 10
- 15. Mathematics Programs 11
- 16. Statistics Programs 11
- B. User Memory and the Stack 12
- C. More about Solving 13
- D. More about Integration 13
- E. Messages 13
- F. Operation Index 13
- Basic Operation 15
- Getting Started 17
- Alpha Keys 18
- Backspacing and Clearing 18
- Getting Started 1–3 19
- Keys for Clearing 19
- Key Description 19
- 1–5 PICTURE 20
- Exiting Menus 23
- Annunciator 23
- 1–8 Getting Started 24
- HP 32SII Annunciator 24
- Upper Row: 24
- Keying in Numbers 25
- Making Numbers Negative 26
- Exponent of Ten 26
- Understanding Digit Entry 27
- Doing Arithmetic 28
- Two–Number Functions 29
- 1–14 Getting Started 30
- Number of Decimal Places 31
- 1–16 Getting Started 32
- Fractions 33
- 1–18 Getting Started 34
- Calculator Memory 36
- Getting Started 1–21 37
- The Automatic Memory Stack 39
- Clearing the X–Register 40
- Reviewing the stack 41
- How ENTER Works 43
- How CLEAR x Works 45
- The LAST X Register 46
- Reusing Numbers with LAST X 48
- 3947.52704.96 48
- Chain Calculations 50
- Order of Calculation 53
- More Exercises 54
- 5961.0)7.05.12()8.04.5( 54
- )01.271.1()75.215.3(3.4 54
- ]32.0)46.733.8[()2.54(33.8 54
- Storing Data into Variables 57
- Clearing Variables 59
- Storage Arithmetic 60
- Recall Arithmetic 61
- Real–Number Functions 65
- Power Functions 66
- Trigonometry 67
- Trigonometric Functions 68
- Hyperbolic Functions 69
- Percentage Functions 69
- 4–6 Real–Number Functions 70
- To Calculate Press: 70
- Conversion Functions 71
- Time Conversions 73
- Angle Conversions 74
- Probability Functions 75
- Probability Menu 76
- Real–Number Functions 4–13 77
- Parts of Numbers 78
- Names of Function 78
- Fractions in the Display 80
- Accuracy Indicators 81
- 0 7/16 0 7/16 82
- Longer Fractions 82
- Fractions 5–5 83
- Choosing Fraction Format 84
- Rounding Fractions 86
- Fractions in Equations 87
- Fractions in Programs 88
- Entering and Evaluating 89
- Key Operation 92
- Variables in Equations 93
- Number in Equations 93
- Functions in Equations 94
- Parentheses in Equations 95
- Types of Equations 98
- Evaluating Equations 99
- Using ENTER for Evaluation 100
- Keys: Display: Description: 101
- Using XEQ for Evaluation 102
- The Syntax of Equations 103
- Equations Meaning 104
- Order Operation Example 104
- Equation Function 105
- 1.&22 106
- P=A+B+Hx(1 SIN(T)+1 SIN(F)) 107
- Verifying Equations 108
- Solving Equations 111
- 7–2 Solving Equations 112
- Solving Equations 7–3 113
- 7–4 Solving Equations 114
- Keys: Display: Description: 114
- Solving Equations 7–5 115
- Verifying the Result 116
- Solving Equations 7–7 117
- 7–8 Solving Equations 118
- Solving Equations 7–9 119
- 7–10 Solving Equations 120
- For More Information 121
- Integrating Equations 123
- Integrating Equations ( 124
- )sincos( 125
- 8–4 Integrating Equations 126
- Accuracy of Integration 128
- Interpreting Accuracy 129
- 8–8 Integrating Equations 130
- Operations with Comb Numbers 133
- Complex Operations 135
- BASE Menu 141
- Menu label Description 141
- Negative Numbers 144
- Range of Numbers 145
- Statistical Operations 149
- Entering One–Variable Data 150
- Entering Two–Variable Data 150
- Statistical Operations 11–3 151
- Initial x, y Corrected x, y 151
- Statistical Calculations 152
- Statistical Operations 11–5 153
- Sample Standard Deviation 154
- Linear regression 155
- Statistical Operations 11–9 157
- 11–10 Statistical Operations 158
- 11–12 Statistical Operations 160
- Statistics Registers 161
- Programming 162
- Simple Programming 163
- Designing a Program 164
- Simple Programming 12–3 165
- Data Input and Output 166
- Entering a Program 167
- Keys That Clear 168
- Function Names in Programs 169
- Running a Program 170
- Executing a Program (XEQ) 171
- Testing a Program 171
- 12–10 Simple Programming 172
- Entering and Displaying Data 173
- 12–12 Simple Programming 174
- Simple Programming 12–13 175
- 12–14 Simple Programming 176
- Simple Programming 12–15 177
- 12–16 Simple Programming 178
- Simple Programming 12–17 179
- Error Stops 180
- Editing Program 181
- Program Memory 182
- Simple Programming 12–21 183
- The Checksum 184
- Nonprogrammable Functions 185
- Programming with BASE 185
- 12–24 Simple Programming 186
- Simple Programming 12–25 187
- 12–26 Simple Programming 188
- Simple Programming 12–27 189
- Programming Techniques 191
- 13–2 Programming Techniques 192
- Branching (GTO) 195
- Using GTO from the Keyboard 196
- Conditional Instructions 197
- Tests of Comparison (x 198
- Programming Techniques 13–9 199
- 13–10 Programming Techniques 200
- 13–12 Programming Techniques 202
- FLAGS Menu 202
- Menu Key Description 202
- Program Lines: Description: 203
- 13–14 Programming Techniques 204
- Conditional Loops (GTO) 206
- Program lines: Description: 207
- 13–18 Programming Techniques 208
- The Variable "i" 210
- The Indirect Address, (i) 211
- Program Control with (i) 212
- Equations with (i) 214
- Solving and Integrating 217
- Programs 217
- Using SOLVE in Program 221
- Integrating a Program 223
- Mathematics Programs 227
- 15–4 Mathematics Programs 230
- Program Lines: Description 230
- Mathematics Programs 15–5 231
- 15–6 Mathematics Programs 232
- Mathematics Programs 15–7 233
- 15–8 Mathematics Programs 234
- Mathematics Programs 15–9 235
- 15–10 Mathematics Programs 236
- Mathematics Programs 15–11 237
- 15–12 Mathematics Programs 238
- Mathematics Programs 15–13 239
- 15–14 Mathematics Programs 240
- Mathematics Programs 15–15 241
- 15–16 Mathematics Programs 242
- Mathematics Programs 15–17 243
- 15–18 Mathematics Programs 244
- Mathematics Programs 15–19 245
- Polynomial Root Finder 246
- 15–22 Mathematics Programs 248
- Mathematics Programs 15–23 249
- 15–24 Mathematics Programs 250
- Mathematics Programs 15–25 251
- Mathematics Programs 15–27 253
- 15–28 Mathematics Programs 254
- Mathematics Programs 15–29 255
- Terms mid Coefficients 255
- 15–30 Mathematics Programs 256
- Coordinate Transformations 257
- 15–34 Mathematics Programs 260
- Mathematics Programs 15–35 261
- 15–36 Mathematics Programs 262
- 15–38 Mathematics Programs 264
- Statistics Programs 265
- 12 266
- Statistics Programs 16–3 267
- 16–4 Statistics Programs 268
- Statistics Programs 16–5 269
- 16–6 Statistics Programs 270
- Statistics Programs 16–7 271
- 16–8 Statistics Programs 272
- Statistics Programs 16–9 273
- 16–10 Statistics Programs 274
- Statistics Programs 16–11 275
- Statistics Programs 16–13 277
- Statistics Programs 16–15 279
- 16–16 Statistics Programs 280
- Statistics Programs 16–17 281
- Grouped Standard Deviation 282
- 16–20 Statistics Programs 284
- Statistics Programs 16–21 285
- 16–22 Statistics Programs 286
- Miscellaneous Programs and 287
- Equations 287
- Prime Number Generator 292
- /) 296
- /) 296
- Appendixes and Reference 297
- Support, Batteries 299
- Environmental Limits 300
- A-3 picture 301
- Testing Calculator Operation 302
- The Self–Test 303
- Limited One–Year Warranty 304
- Service Charge 306
- Shipping Instructions 306
- Warranty on Service 306
- Regulatory Information 307
- User Memory and the Stack 309
- Memory Requirements 310
- Resetting the Calculator 311
- Clearing Memory 311
- The Status of Stack Lift 312
- Disabling Operations 313
- Neutral Operations 313
- More about Solving 315
- C–2 More about Solving 316
- Interpreting Results 317
- C–4 More about Solving 318
- More about Solving C–5 319
- More about Solving C–7 321
- When SOLVE Cannot Find Root 322
- C–10 More about Solving 324
- More about Solving C–11 325
- 05.00.3)] (x [x 326
- More about Solving C–13 327
- Round–Off Error 328
- Underflow 329
- More about Integration 331
- D–2 More about Integration 332
- More about Integration D–3 333
- D–4 More about Integration 334
- More about Integration D–5 335
- D–6 More about Integration 336
- D–8 More about Integration 338
- More about Integration D–9 339
- D–10 More about Integration 340
- Messages 341
- E–2 Messages 342
- Messages E–3 343
- E–4 Messages 344
- Operation Index 345
- F–4 Operation Index 348
- Operation Index F–5 349
- Operation Index F–7 351
- F–8 Operation Index 352
- Operation Index F–11 355
- F–12 Operation Index 356
- F–14 Operation Index 358
- Special characters 361
- Index–2 362
- Index–3 363
- Index–4 364
- Index–5 365
- Index–6 366
- Index–7 367
- Index–8 368
- Index–9 369
- Index–10 370
- Index–11 371
- Index–12 372
- Index–13 373
- Index–14 374
- Index–15 375
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