Textbook pdf's

More documents

Recommendations

Info

To graph the second derivative, enter nDeriv(Y2(X), X, X) in Y3. (See step 2.) Remember to select Y2 from the Function menu. You can deselect a function to be graphed. Position the cursor over the equal sign of the desired function in the equation editor. Press ENTER . Only the functions whose equal signs are shaded will be graphed when GRAPH is pressed. PART 2 USING THE GEOMETER’S SKETCHPAD 18 Graphing a Function 1. Turn on the grid. From the Graph menu, choose Show Grid. 2. Enter the function. From the Graph menu, choose Plot New Function. The function calculator should appear. 3. Graph the function y x 2 3x 2. NEL REVIEW OF TECHNICAL SKILLS APPENDIX 609
Use either the calculator keypad or the keyboard to enter x ^ 2 - 3 * x 2. Then press OK on the calculator keypad. The graph of y x 2 3x 2 should appear on the grid. 4. Adjust the origin and/or scale. To adjust the origin, left-click on the point at the origin to select it. Then left-click and drag the origin as desired. To adjust the scale, left-click in blank space to deselect, and then left-click on the point at (1, 0) to select it. Left-click and drag this point to change the scale. 610 REVIEW OF TECHNICAL SKILLS APPENDIX NEL
Page 1 and 2:
Chapter 1 INTRODUCTION TO CALCULUS
Page 3 and 4:
y x 3 1 , if 3 6 t 6 0 t 6. A func
Page 5 and 6:
What Is Calculus? Two simple geomet
Page 7 and 8:
If a and b were radicals, squaring
Page 9 and 10:
Exercise 1.1 PART A 1. Write the co
Page 11 and 12:
Consider a curve y f 1x2 and a poi
Page 13 and 14:
EXAMPLE 2 Tech Support For help gra
Page 15 and 16:
The slope of the tangent at 13, 42
Page 17 and 18:
INVESTIGATION 4 Tech Support For he
Page 19 and 20:
4. Simplify each of the following d
Page 21 and 22:
18. Copy the following figures. Dra
Page 23 and 24:
A. Determine the average velocity o
Page 25 and 26:
Instantaneous Velocity The velocity
Page 27 and 28:
Solution a. C11002 10V100 1000 1
Page 29 and 30:
Exercise 1.3 C PART A 1. The veloci
Page 31 and 32:
f 1x2 f 1a2 15. Use the alternate
Page 33 and 34:
. Use your results for part a to ap
Page 35 and 36:
The graph shown on your calculator
Page 37 and 38:
limits because, in each case, only
Page 39 and 40:
11. For each function, sketch the g
Page 41 and 42:
EXAMPLE 2 EXAMPLE 3 EXAMPLE 4 Using
Page 43 and 44:
INVESTIGATION Here is an alternate
Page 45 and 46:
In this section, we learned the pro
Page 47 and 48:
A 11. Jacques Charles (1746-1823) d
Page 49 and 50:
A second condition for continuity a
Page 51 and 52:
d. The function F is not continuous
Page 53 and 54:
x 3, if x 3 12. g1x2 e 2 k, if
Page 55 and 56:
Key Concepts Review We began our in
Page 57 and 58:
c. What is the present rate of chan
Page 59 and 60:
16. Evaluate the limit of each diff
Page 61 and 62:
Chapter 2 DERIVATIVES Imagine a dri
Page 63 and 64:
2 4 5. Expand, and collect like te
Page 65 and 66:
Section 2.1—The Derivative Functi
Page 67 and 68:
For the Parabola f1x2 x 2 The slop
Page 69 and 70:
Note that f 1t2 Vt is defined for
Page 71 and 72:
EXAMPLE 6 Reasoning about different
Page 73 and 74:
Exercise 2.1 PART A 1. State the do
Page 75 and 76:
T 15. Match each function in graphs
Page 77 and 78:
EXAMPLE 1 Applying the constant fun
Page 79 and 80:
We conclude this section with the s
Page 81 and 82:
EXAMPLE 6 Connecting the derivative
Page 83 and 84:
x 1 8. Determine the slope of the
Page 85 and 86:
Section 2.3—The Product Rule In t
Page 87 and 88:
EXAMPLE 3 Selecting an efficient st
Page 89 and 90:
EXAMPLE 6 Selecting a strategy to d
Page 91 and 92:
PART B dy 5. Determine the value of
Page 93 and 94:
9. Determine the equation of the ta
Page 95 and 96:
EXAMPLE 1 Applying the quotient rul
Page 97 and 98:
Exercise 2.4 PART A 1. What are the
Page 99 and 100:
Section 2.5—The Derivatives of Co
Page 101 and 102:
with respect to x is equal to the p
Page 103 and 104:
EXAMPLE 7 Combining derivative rule
Page 105 and 106:
Exercise 2.5 PART A 1. Given f 1x2
Page 107 and 108:
Technology Extension: Derivatives o
Page 109 and 110:
Key Concepts Review Now that you ha
Page 111 and 112:
9. For what values of x does the cu
Page 113 and 114:
24. At a manufacturing plant, produ
Page 115 and 116:
Chapter 3 DERIVATIVES AND THEIR APP
Page 117 and 118:
4. Determine the area of each figur
Page 119 and 120:
Section 3.1—Higher-Order Derivati
Page 121 and 122:
Motion on a Straight Line An object
Page 123 and 124:
d. The object moves in a positive d
Page 125 and 126:
EXAMPLE 5 Analyzing motion under gr
Page 127 and 128:
Exercise 3.1 C K PART A 1. Explain
Page 129 and 130:
T 12. A dragster races down a 400 m
Page 131 and 132:
H. Repeat part D for the following
Page 133 and 134:
Only t 3 is in the given interval,
Page 135 and 136:
IN SUMMARY Key Ideas • The maximu
Page 137 and 138:
T PART B 4. Using the algorithm for
Page 139 and 140:
Mid-Chapter Review 1. Determine the
Page 141 and 142:
Section 3.3—Optimization Problems
Page 143 and 144:
For extreme values, set V¿1x2 0.
Page 145 and 146:
Exercise 3.3 C PART A 1. A piece of
Page 147 and 148:
a. Determine the dimensions that sh
Page 149 and 150:
The revenue function is R1x2 17 0
Page 151 and 152:
The minimal cost is approximately $
Page 153 and 154:
T C 8. The fuel cost per hour for r
Page 155 and 156:
CAREER LINK WRAP-UP Investigate and
Page 157 and 158:
10. For each of the following cost
Page 159 and 160:
s1t2 t 26. Find the absolute maxi
Page 161 and 162:
Chapter 4 CURVE SKETCHING If you ar
Page 163 and 164:
5. Determine the derivative of each
Page 165 and 166:
Section 4.1—Increasing and Decrea
Page 167 and 168:
dy Since this is a polynomial funct
Page 169 and 170:
IN SUMMARY Key Ideas • A function
Page 171 and 172:
9. Each of the following graphs rep
Page 173 and 174:
Solution dy First determine dx . dy
Page 175 and 176:
Note that there is no value of x fo
Page 177 and 178:
EXAMPLE 4 Graphing the derivative g
Page 179 and 180:
4. Find the x- and y-intercepts of
Page 181 and 182:
Section 4.3—Vertical and Horizont
Page 183 and 184:
The behaviour of the graph can be i
Page 185 and 186:
EXAMPLE 2 Expressing a polynomial f
Page 187 and 188:
When lim f 1x2 k or lim f 1x2 k,
Page 189 and 190:
For horizontal asymptotes, 3x f 1x2
Page 191 and 192:
Now let's consider the straight lin
Page 193 and 194:
Exercise 4.3 PART A 1. State the eq
Page 195 and 196:
12. Use the features of each functi
Page 197 and 198:
11. a. What does f ¿1x2 7 0 imply
Page 199 and 200:
From these investigations, we can m
Page 201 and 202:
Setting dy dx 0, we obtain 3 1x 2
Page 203 and 204:
The second derivative of f 1x2 is f
Page 205 and 206:
Exercise 4.4 K PART A 1. For each f
Page 207 and 208:
Section 4.5—An Algorithm for Curv
Page 209 and 210:
Therefore, by the second derivative
Page 211 and 212:
Interval 1, 12 11, 0.82 10.8, 22 12
Page 213 and 214:
K A 1x PART B 4. Use the algorithm
Page 215 and 216:
Key Concepts Review In this chapter
Page 217 and 218:
5. For each of the following, check
Page 219 and 220:
17. If f 1x2 x3 8 , determine the
Page 221 and 222:
Chapter 5 DERIVATIVES OF EXPONENTIA
Page 223 and 224:
Radian Measure A radian is the meas
Page 225 and 226:
5. Convert the following angles to
Page 227 and 228:
Section 5.1—Derivatives of Expone
Page 229 and 230:
From the investigation, you should
Page 231 and 232:
EXAMPLE 4 Connecting the derivative
Page 233 and 234:
A C PART B 6. Determine the equatio
Page 235 and 236:
Section 5.2—The Derivative of the
Page 237 and 238:
In general, for the exponential fun
Page 239 and 240:
Solution a. January 1, 1900, is exa
Page 241 and 242:
Section 5.3—Optimization Problems
Page 243 and 244:
The average revenue to the company
Page 245 and 246:
Exercise 5.3 PART A 1. Use graphing
Page 247 and 248:
12. Find the maximum and minimum va
Page 249 and 250:
9. The rapid growth in the number o
Page 251 and 252:
INVESTIGATION 2 A.Using your graphi
Page 253 and 254:
With practice, you will learn how t
Page 255 and 256:
We evaluate f 1x2 at the critical n
Page 257 and 258:
A T 6. Determine the absolute extre
Page 259 and 260:
Derivatives of Composite Functions
Page 261 and 262:
Page 263 and 264:
Review Exercise 1. Differentiate ea
Page 265 and 266:
18. The position of a particle is g
Page 267 and 268:
Chapter 5 Test dy 1. Determine the
Page 269 and 270:
8. Use algebraic methods to evaluat
Page 271 and 272:
f 1x2 142e 5x1 24. For each functi
Page 273 and 274:
Review of Prerequisite Skills In th
Page 275 and 276:
CAREER LINK Investigate CHAPTER 6:
Page 277 and 278:
What is a Vector? A vector is a mat
Page 279 and 280:
EXAMPLE 1 B A E D C Connecting vect
Page 281 and 282:
A K B 5. Given the vector AB ! as s
Page 283 and 284:
Section 6.2—Vector Addition In th
Page 285 and 286:
the overall magnitude would be equa
Page 287 and 288:
Solution c b a a - b + c a - b c a
Page 289 and 290:
W N S E The vectors are drawn so th
Page 291 and 292:
Exercise 6.2 PART A 1. The vectors
Page 293 and 294:
10. a. In ! the ! example ! involvi
Page 295 and 296:
0 0 The previous example illustrate
Page 297 and 298:
Solution a. 30˚ y x 2x-y 2x -y 30
Page 299 and 300:
Solution Draw a sketch and determin
Page 301 and 302:
8. The two vectors a ! and b ! are
Page 303 and 304:
Section 6.4—Properties of Vectors
Page 305 and 306:
Demonstrating the distributive law
Page 307 and 308:
IN SUMMARY Key Idea • Properties
Page 309 and 310:
Mid-Chapter Review 1. ABCD is a par
Page 311 and 312:
Section 6.5—Vectors in R 2 and R
Page 313 and 314:
Right-Handed System of Coordinates
Page 315 and 316:
Solution a. A16, 0, 02 is a point o
Page 317 and 318:
There is one further observation th
Page 319 and 320:
C A 14. a. What is the equation of
Page 321 and 322:
R 2 EXAMPLE 1 Representing vectors
Page 323 and 324:
EXAMPLE 2 Representing the sum and
Page 325 and 326:
EXAMPLE 5 Calculating the magnitude
Page 327 and 328:
A 10. Parallelogram is determined b
Page 329 and 330:
EXAMPLE 1 Representing vectors in R
Page 331 and 332:
. Using components, a ! b ! c !
Page 333 and 334:
IN SUMMARY Key Ideas • In R 3 , i
Page 335 and 336:
Section 6.8—Linear Combinations a
Page 337 and 338:
In R 2 , it is possible to take any
Page 339 and 340:
Geometrically, the linear combinati
Page 341 and 342:
IN SUMMARY Key Ideas • In R 2 , O
Page 343 and 344:
Page 345 and 346:
Review Exercise 1. Determine whethe
Page 347 and 348:
15. A rectangular prism measuring 3
Page 349 and 350:
Chapter 6 Test 1. The vectors a ! ,
Page 351 and 352:
Page 353 and 354:
Section 7.1—Vectors as Forces The
Page 355 and 356:
of 6 cm, also pointing east. The ve
Page 357 and 358:
is drawn approximately to scale, an
Page 359 and 360:
The magnitude of the vertical compo
Page 361 and 362:
! T1 sin 105° 1961sin 45°2 T ! 1
Page 363 and 364:
49 34 30 cos CBA 1 cos CBA 2 120
Page 365 and 366:
C T f 3 40 N O 35 N 45° 30 N f 2 2
Page 367 and 368:
Solution We start by drawing positi
Page 369 and 370:
v a v + w w 20 triangles, Solving t
Page 371 and 372:
A T C 9. A small airplane has an ai
Page 373 and 374:
Perhaps the most important observat
Page 375 and 376:
If we look at the right-angled tria
Page 377 and 378:
Solution Consider the following dia
Page 379 and 380:
A T 10. What is the value of the do
Page 381 and 382:
Expanding, we get b 2 1 2a 1 b 1
Page 383 and 384:
. 0 a ! 0 2 @b ! 112 2 122 2 142
Page 385 and 386:
One of the most important propertie
Page 387 and 388:
4. a. From the set of vectors e11,
Page 389 and 390:
Mid-Chapter Review 1. a. If 0 a ! 0
Page 391 and 392:
Section 7.5—Scalar and Vector Pro
Page 393 and 394:
EXAMPLE 1 Reasoning about the chara
Page 395 and 396:
x EXAMPLE 3 z P (2, 1, 4) g b a O(0
Page 397 and 398:
EXAMPLE 4 Calculating a specific di
Page 399 and 400:
IN SUMMARY Key Idea • A projectio
Page 401 and 402:
B C 12. In the diagram shown, ^ ABC
Page 403 and 404:
a 3 b, k = 1 O b 3 a, k = -1 b a is
Page 405 and 406:
If we carry out an identical proced
Page 407 and 408:
EXAMPLE 2 Calculating cross product
Page 409 and 410:
K A C T 4. Calculate the cross prod
Page 411 and 412:
EXAMPLE 1 Using the dot product to
Page 413 and 414:
. We start by constructing position
Page 415 and 416:
EXAMPLE 4 Using the cross product t
Page 417 and 418:
Page 419 and 420:
Review Exercise 1. Given that a !
Page 421 and 422:
18. For the vectors m ! 1 V3, 2, 3
Page 423 and 424:
Chapter 7 Test 1. Given the vectors
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Both of these vectors can be multip
Page 431 and 432:
c. If the point Q121, 232 lies on t
Page 433 and 434:
In this section, the vector and par
Page 435 and 436:
C K A T 6. a. If the equation of a
Page 437 and 438:
EXAMPLE 1 Representing the Cartesia
Page 439 and 440:
It is not possible, in this case, t
Page 441 and 442:
AP ! 1x 4, y 1222 1x 4, y 22.
Page 443 and 444:
u cos 1 a 3 12 1 10 21 25 2 b u
Page 445 and 446:
A T 10. For each pair of lines, det
Page 447 and 448:
is its direction vector. If represe
Page 449 and 450:
EXAMPLE 4 Representing the equation
Page 451 and 452:
C A T 6. a. Determine parametric eq
Page 453 and 454:
13. The Cartesian equation of a lin
Page 455 and 456:
s t s(1, 2, 1) t(0, 2, 1), s, tR P
Page 457 and 458:
After deriving vector and parametri
Page 459 and 460:
EXAMPLE 4 Representing the equation
Page 461 and 462:
A K T 7. a. Determine parameters co
Page 463 and 464:
To derive the equation of this plan
Page 465 and 466:
A number of observations can be mad
Page 467 and 468:
When we considered lines in R 2 , w
Page 469 and 470:
IN SUMMARY Key Idea • The Cartesi
Page 471 and 472:
Section 8.6—Sketching Planes in R
Page 473 and 474:
EXAMPLE 2 Representing the graph of
Page 475 and 476:
EXAMPLE 5 Graphing planes whose Car
Page 477 and 478:
IN SUMMARY Key Idea • A sketch of
Page 479 and 480:
Page 481 and 482:
Review Exercise 1. Determine vector
Page 483 and 484:
20. Calculate the acute angle that
Page 485 and 486:
Chapter 8 Test 1. a. Given the poin
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
4 13 s2 211 4s2 12 8s2 8 0 1
Page 493 and 494:
Method 2: Again, this result can be
Page 495 and 496:
We can now select any two of the th
Page 497 and 498:
IN SUMMARY Key Ideas • Line and p
Page 499 and 500:
A T 11. a. Show that the lines and
Page 501 and 502:
equations. Since the lines would be
Page 503 and 504:
Solution 1: Interchange equations 1
Page 505 and 506:
Substituting into the second equati
Page 507 and 508:
1: Multiply equation 1 by k, and ad
Page 509 and 510:
K C PART B 4. Solve each system of
Page 511 and 512:
Section 9.3—The Intersection of T
Page 513 and 514:
If we had solved the system using e
Page 515 and 516:
then x 3s 1. Now it is a matter o
Page 517 and 518:
Exercise 9.3 C K PART A 1. A system
Page 519 and 520:
Mid-Chapter Review 1. Determine the
Page 521 and 522:
Section 9.4—The Intersection of T
Page 523 and 524:
1: Create two new equations, 4 and
Page 525 and 526:
Thus, 7y 5t 3. Dividing by 7, we g
Page 527 and 528:
Inconsistent Systems for Three Equa
Page 529 and 530:
Therefore, we can choose ! ! ! m 1
Page 531 and 532:
Exercise 9.4 PART A 1. A student is
Page 533 and 534:
9. Solve each system of equations u
Page 535 and 536:
Section 9.5—The Distance from a P
Page 537 and 538:
EXAMPLE 1 Calculating the distance
Page 539 and 540:
In triangle PQR, sin u d @ QP ! @
Page 541 and 542:
Exercise 9.5 PART A 1. Determine th
Page 543 and 544:
Section 9.6—The Distance from a P
Page 545 and 546:
It is also possible to use the dist
Page 547 and 548:
p 1 p 2 U V d L 1 : r = (-2, 1, 0)
Page 549 and 550:
The required distance between the t
Page 551 and 552:
K A T PART B 2. Determine the follo
Page 553 and 554:
Review Exercise 1. The lines 2x y
Page 555 and 556:
14. You are given the lines , and r
Page 557 and 558:
Chapter 9 Test 1. a. Determine the
Page 559 and 560: P(1, -2, 4) Q P9 2x - 3y - 4z + 66
Page 561 and 562: 29. A line that passes through the
Page 563 and 564: Solution a. Differentiate both side
Page 565 and 566: Exercise PART A 1. State the chain
Page 567 and 568: dA b. To determine differentiate A
Page 569 and 570: 1 16 dh dt Therefore, at the momen
Page 571 and 572: 11. Two cyclists depart at the same
Page 573 and 574: Solution a. y ln15x2 Using the cha
Page 575 and 576: x1x 42 0 x 4 or x 0 But x 0 is
Page 577 and 578: The Derivatives of General Logarith
Page 579 and 580: The Derivative of a Composite Funct
Page 581 and 582: To solve this, we take the natural
Page 583 and 584: Exercise PART A 1. Differentiate ea
Page 585 and 586: y eliminating unknowns. In Example
Page 587 and 588: Properties of a Matrix in Row-Echel
Page 589 and 590: Exercise PART A 1. Write an augment
Page 591 and 592: 12. Determine the equation of the p
Page 593 and 594: 1 0 0 18 4 (row 3) row 1 £ 0 1 0
Page 595 and 596: Finally, convert the entry in the s
Page 597 and 598: Review of Technical Skills Appendix
Page 599 and 600: 3 Evaluating a Function 1. Enter th
Page 601 and 602: 7 Making a Table of Differences To
Page 603 and 604: 4. Cursor along the curve to any po
Page 605 and 606: 5. Display and analyze the results.
Page 607 and 608: 14 Graphing a Trigonometric Functio
Page 609: 2. Enter the second equation. Press
Page 613 and 614: 20 Graphing the Derivative of a Fun
Page 615 and 616: 4. Create a function. Right-click t
Page 617 and 618: composition: the process of combini
Page 619 and 620: G geometric vectors: vectors that a
Page 621 and 622: ationalizing the denominator: the p
Page 623 and 624: Answers Chapter 1 0 0 0 0 0 Review
Page 625 and 626: d. about 1 e. about 7 8 f. no tang
Page 627 and 628: d. 13. m 3; b 1 14. a 3, b 2, c
Page 629 and 630: Review Exercise, pp. 56-59 1. a. 3
Page 631 and 632: 19. a. y 7 b. y 5x 5 c. y 18x 9
Page 633 and 634: 20. a. 34.3 m> s b. 39.2 m> s c. 54
Page 635 and 636: 17. a. 100 bacteria b. 1200 bacteri
Page 637 and 638: 11. a. b. 160x y 16 0 60x y 61
Page 639 and 640: 3. 1 2x 4. a. x 2 15x 6 b. 6012x
Page 641 and 642: 14. t 1 s; away 15. a. s1t2 kt 2
Page 643 and 644: 14. a. triangle side length 0.96 cm
Page 645 and 646: Review Exercise, pp. 156-159 11. 20
Page 647 and 648: c. i. ii. iii. d. i. ii. iii. 5 4 3
Page 649 and 650: . local minimum: 11.41, 39.62, loca
Page 651 and 652: 2. increasing: x 6 1 and x 7 2, dec
Page 653 and 654: to a zero of its derivative, the nu
Page 655 and 656: 7. (-2, 10) 10 8 y 10. a. 8 y e. 4
Page 657 and 658: 4. hole at x 2; large and negative
Page 659 and 660: sin x b. 1 sin 2 tan x sec x x L
Page 661 and 662:
12. a. no maximum or minimum value
Page 663 and 664:
Review Exercise, pp. 263-265 1. a.
Page 665 and 666:
x 2. 5. a. 19 000 fish> year b. 23
Page 667 and 668:
Section 6.1, pp. 279-281 6. a. b. c
Page 669 and 670:
17. P G 4. Answers may vary. For ex
Page 671 and 672:
11. a. AG ! a ! b ! c ! , b. AG
Page 673 and 674:
d. OD ! 11, 1, 12 (0, 0, 1) (1, 0,
Page 675 and 676:
Section 6.7, pp. 332-333 1. a. 1i !
Page 677 and 678:
24. 25. a. 0a ! b. 0a ! 0 2 0b !
Page 679 and 680:
. Since the equilibrant is directed
Page 681 and 682:
7. a. scalar projection: 0, vector
Page 683 and 684:
2. a. 3 b. 7 c. 43 d. 217 e. 5 f. 1
Page 685 and 686:
cos A 1 cos B 1 cos C 1 area of t
Page 687 and 688:
. r ! 11, 1, 02 t10, 1, 12, tR; x
Page 689 and 690:
2. 12, 3, 42 3. P must lie on plane
Page 691 and 692:
25. A plane has two parameters, bec
Page 693 and 694:
coincident with the plane, meaning
Page 695 and 696:
Mid-Chapter Review, pp. 518-519 1.
Page 697 and 698:
8. a. b. y 1 z 1 4 , 2 c. x 3t
Page 699 and 700:
10. vector equation: r ! 10, 0, 42
Page 701 and 702:
. 23. a. b. 2a 1 2 b a 6 7 , 2 7 ,
Page 703 and 704:
16. 17. 18. 19. 2 3 4 m>min 144 m>m
Page 705 and 706:
ln x 1 e. ln 2 4x 1 x ln 13x 2 2
Page 707 and 708:
Index A Absolute extrema, 130, 132,
Page 709:
normal, 461-469, 486, 512, 524 para
show all

Textbook pdf's

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?