HP 15C Manual de usuario Pagina 183
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Section 13: Finding the Roots of an Equation 183
Keystrokes
Display
´_ 0
5.0000
The desired root.
After the routine finds and displays the root, you can ensure that the
displayed number is indeed a root of f(x) = 0 by checking the stack. You have
seen that the display (X-register) contains the desired root. The Y-register
contains a previous estimate of the root, which should be very close to the
displayed root. The Z-register contains the value of your function
evaluated at the displayed root.
Keystrokes
Display
)
5.0000
A previous estimate of the
root.
)
0.0000
Value of the function at the
root showing that f(x) = 0.
Quadratic equations, such as the one you are solving, can have two roots. If
you specify two new initial estimates, you can check for a second root. Try
estimates of 0 and -10 to look for a negative root.
Keystrokes
Display
0 v
0.0000
Initial estimates.
10 “
–10
´ _ 0
–2.0000
The second root.
)
–2.0000
A previous estimate of the
root.
)
0.0000
Value of f(x) at second root.
- Owner’s Handbook 1
- Legal Notice 2
- Introduction 3
- Contents 4
- Contents 7 7
- 8 Contents 8
- Contents 9 9
- The HP-15C: 12
- A Problem Solver 12
- Manual Solutions 13
- Programmed Solutions 14
- Getting Started 18
- Prefix Keys 19
- Keying in Exponents 19
- The “CLEAR” Keys 20
- Display Clearing: ` and − 21
- Calculations 22
- 5998.0)]7.05.12()8.04.5[( 23
- Numeric Functions 24
- Trigonometric Operations 26
- Time and Angle Conversions 26
- Degrees/Radians Conversions 27
- Logarithmic Functions 28
- Hyperbolic Functions 28
- The Automatic Memory Stack 32
- LAST X, and Data Storage 32
- The LAST X Register and K 35
- Order of Entry and the v Key 37
- Nested Calculations 38
- Storage Register Operations 42
- Error 3 43
- Probability Calculations 47
- Random Number Generator 48
- Accumulating Statistics 49
- Standard Deviation 53
- Linear Regression 54
- Other Applications 57
- The Display 58
- Scientific Notation Display 59
- Engineering Notation Display 59
- Special Displays 60
- Digit Separators 61
- Error Display 61
- Overflow and Underflow 61
- Continuous Memory 62
- Resetting Continuous Memory 63
- Programming Basics 66
- Intermediate Program Stops 68
- Running a Program 68
- How to Enter Data 69
- Memory Configuration 75
- Initial Memory Configuration 76
- Program Boundaries 77
- Unexpected Program Stops 78
- Abbreviated Key Sequences 78
- User Mode 79
- Nonprogrammable Functions 80
- Program Editing 82
- Line Position 86
- to run 88
- Program Branching 90
- Example: Flags 95
- Looping 98
- Conditional Branching 98
- Subroutines 101
- Examples 102
- Further Information 105
- The Index Register 106
- The Mechanics 107
- Index Register Arithmetic 108
- Exchanging the X-Register 108
- Indirect Branching With V 108
- Indirect Flag Control With V 109
- Example: Loop Control with e 112
- test (goal) value 113
- Indirect Display Control 116
- Calculating With 120
- Complex Numbers 120
- Deactivating Complex Mode 121
- Entering Complex Numbers 121
- Stack Lift in Complex Mode 124
- Changing Signs 124
- Clearing a Complex Number 125
- Entering a Real Number 128
- One-Number Functions 131
- Two-Number Functions 131
- Stack Manipulation Functions 131
- Conditional Tests 132
- Error 0 133
- Problems 135
- )6 (-82 136
- For Further Information 137
- Calculating With Matrices 138
- Matrix Dimensions 140
- Dimensioning a Matrix 141
- Displaying Matrix Dimensions 142
- Changing Matrix Dimensions 142
- and R 146
- Matrix Operations 147
- The Result Matrix 148
- Copying a Matrix 149
- One-Matrix Operations 149
- Scalar Operations 151
- Arithmetic Operations 153
- Matrix Multiplication 154
- and BA 155
- Solving the Equation AX = B 156
- Calculating the Residual 159
- Using Matrices in LU Form 160
- 22222121 162
- 12121111 162
- 2 to transform Z 165
- Memory Allocation 171
- 4 to calculate X 172
- , -, * 173
- Summary of Matrix Functions 177
- Finding the Roots 180
- t / 20 185
- When No Root Is Found 186
- Error 8 187
- Choosing Initial Estimates 188
- letter label or G label 191
- Using _ in a Program 192
- Restriction on the Use of _ 193
- Memory Requirements 193
- Numerical Integration 194
- . )sin - ( cos 197
- dθθxxJ 197
- Accuracy of f 200
- 1.6054 ± 0.0001, the 201
- Using f in a Program 203
- Error Conditions 205
- Pr Error (Power Error) 208
- Stack Lift and 209
- Disabling Operations 210
- Enabling Operations 210
- Neutral Operations 211
- LAST X Register 212
- through R 214
- Memory Reallocation 215
- Restrictions on Reallocation 216
- Program Memory 217
- 23 if executed 218
- A Detailed Look at _ 220
- Error 8 is 221
- Accuracy of the Root 222
- produces a root of 223
- Interpreting Results 226
- routine has 229
- or any 229
- Finding Several Roots 233
- Limiting the Estimation Time 238
- For Advanced Information 239
- A Detailed Look at f 240
- )sin4cos( d 242
- )( xxfxF 246
- 10100.5)δ( 247
- (x) in roughly the same 248
- (x) ~ 10 248
- Batteries 259
- Function Summary and Index 262
- Computes natural 263
- Mathematics 264
- Matrix Functions 264
- Number Alteration 265
- Percentage 266
- Probability 266
- Manipulation 266
- Statistics 267
- Storage 267
- Trigonometry 268
- Programming Summary and Index 269
- Is flag set? Tests 270
- Subject Index 271
- Product Regulatory & 284
- Environment Information 284
- Logo, United States Only 285
- Canadian Notice 285
- Avis Canadien 285
- Chemical Substances 288
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