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16-22 Step-by-Step Examples
Exercise 8 For this exercise, make sure that the calculator is in exact
real mode with X as the current variable.
Part 1 For an integer, n, define the following:
Define g over [0,2] where:
1. Find the variations of g over [0,2]. Show that for
every real x in [0,2]:
2. Show that for every real x in [0,2]:
3. After integration, show that:
4. Using:
show that if has a limit L as n approaches infinity,
then:
u
n
2x 3+
x 2+
---------------
e
x
n
---
xd
0
2
∫
=
gx()
2x 3+
x 2+
---------------
=
3
2
---
gx()
7
4
---
≤≤
3
2
---
e
x
n
---
gx()e
x
n
---
7
4
---
e
x
n
---
≤≤
3
2
---
ne
2
n
---
n–
⎝⎠
⎜⎟
⎛⎞
u
n
7
4
---
ne
2
n
---
n–
⎝⎠
⎜⎟
⎛⎞
≤≤
e
x
1–
x
-------------
x 0→
lim 1=
u
n
3 L
7
2
---
≤≤
hp40g+.book Page 22 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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