[PDF] Answers No. Exercise Je jJ. 7.

View - Download Answers

Previous PDF

Next PDF

Answers to Exercises

I am much indebted to Anthony Petrello for some of the answers to the exer cises.

I, §2, p. 13

1. -3 < x < 3 2. - 1 x

0 3. -j3 x -1 or 1 x j3

4. x < 3 or x > 7 5. - 1 < x < 2 6. x < -lor

x > 1 7. - 5 < x < 5

8. - 1 x 0 9. x 1 or x = 0 10. x -10 or x = 5

11. x -10 or x = 5 12. x 1 or x = -! 13. x < -4

14. -5

17. -2 < x < 8 18. 2 < x < 4 19. -4 < x < 10 20. x < -4 and x> 10

21. x < -10 and x > 4

I, §3, p. 17

1.

2. (2x 1) 3. 0, 2, 108 4. 2z -Z2, 2w - w

2

5. x # j2 or -j2. f(5) = b 6. All x. f(27) = 3

7. (a)

1 (b) 1 (c) -1 (d) -1 8. (a) 1 (b) 4 (c) 0 (d) 0

9. (a) -2 (b) -6 (c) x2+4x-2 10. 2

II. (a) odd (b) even (c) odd (d) odd

I, §4, p. 20

1. 8 and 9 2.! and -1 3. /6 and 2 4. and 2

1/3

5. -h and! 6. 9 and 8

7. -! and -1 8.! and! 9. 1 and -! 10. -5:2 and!

A2 ANSWERS TO EXERCISES

II. Yes. Suppose a is negative, so write a = -b where b is positive. Let c be a positive number such that c" = b. Then (-c)" = a because (-1)" = -1 since n is odd.

II, §1, p. 24

3. x negative, y positive 4. x negative, y negative

II, §3, p. 33

5. y = + i 6. y = -ix + S 7. x = J2

9 9j3

8. y = --;:;-x + 4 ---;:;-9. y = 4x -3 10. y = -2x + 2

",3+3 ",3+3

II. y= -!x+3+ J'!-12. y=j3x+S+j3 19. -! 20.-8

21. 2 + j2 22.!<3 + j3) 23. y = (x -n>(J22_ n) + 1

24. 25. y= -(x+ l)(j23+ 1)+2

26. y = (x + 1)(3 + j2) + j2 29. (a) x = -4, y = -7 (b) x = y = i

(c) x = -!, y = 1 (d) x = -6, Y = -5

II, §4, p. 35

1.J97 2.j2 3.Js2 4.Ji3 5.!j5 6.(4,-3) 7. SandS 8.(-2,5)

9. Sand 7

II, §8, p. 51

5. (x -2)2 + (y + 1)2 = 25 6. x

2 + (y -

1)2 = 9 7. (x + \)2 + y2 = 3

8. y + ¥ = 2(x + W 9. y - 1 = (x + 2)2 10. y + 4 = (x -\)2

II. (x + 1)2 + (y -2)2 = 2 12. (x -2)2 + (y -\)2 = 2

13. x + ¥-= 2(y + !)2 14. x-I = (y + 2)2

III, §1, p. 61

1. 4 2. -2 3. 2 4. i S. -! 6. 0 7. 4 8. 6 9. 3 10. 12 II. 2

12. 3 13. a

ANSWERS TO EXERCISES

III, §2, p. 70

Tangent line at x = 2 Slope at x = 2

1. 2x y = 4x - 3 4

2. 3x2 y = 12x -16 12

3. 6x2 y = 24x -32 24

4.6x y = 12x -12 12

5.2x y = 4x - 9 4

6. 4x + I Y = 9x - 8 9

7. 4x -3 Y = 5x - 8 5

3x2

8. 2+2 y = 8x - 8 8

9. Y = + 1 -(x + 1)2 -9 2

Y = +.!j

2 10. - (x + 1)2 -9

III, §3, p. 75

2 I 1

I. 4x + 3 2. -2 3. 2 4. 2x + 1 5. -2 6. 9x

2 (2x + 1) (x + 1) (2x -1) 3x 2

10. 2 + I 11. _2/X2 12. -3/x

2

13. -2/(2x -W 14. -3/(3x + 1)2 15. -1/(x + 5)2 16. -I/(x _ 2)2

17. -2x-3 18. -2(x + 1)-3

III, §4, p. 78

1. X4 + 4x

3h + 6x 2 h 2 + 4xh3 + h4 2. 4x3

3. (a) jx-

I/3 (b) (c) 4. Y = 9x -8 5. Y = tx + t slope t -3 7 -3 1 -fi 1

6. Y = Y x + 32' slope y 7. Y = 2-fi x + 2' slope 2-fi

8. (a) !5-

3/4 (b) _!r 5/4 (c) )2(\0)2-1) (d) n7 n-1

III, §5, p. 89

l. (a) (b) £X- 1/4 (c) x (d) £x 2

2. (a) 55x'O (b) -8x-

3 (c) -15x2 + 2x

3. (a) -iX-

7/4 (b) 3 -

6x 2 (c) 20x 4 - 21x
2 + 2

4. (a) 21x2 + 8x (b) + 20x

3 - 3x 2 + 3

5. (a) -25x-

2 + 6X-

I/2 (b)

6x2 + 35x

6 (c) 16x 3 - 21x

2 + 1

6. (a) -16x

7 (b) 12x 3 -

4x + 1 (c) 7nx

6 -

40x4 + 1

7. (x3 + x) + (3x2 + I )(x -I) 8. (2x

2 -

I )4x3 + 4x(x4 + I)

9. (x + 1)(2x + ¥Xl/l) + (Xl + 5XJ/l)

10. (2x -5)(l2x

3 + 5) + 2(3x4 + 5x + 2) A3

A4 ANSWERS TO EXERCISES

(_2X2 + 2)

14. 2 2

(X + 3x + 1) (t + 1)(t -1)(2t + 2) -(t 2 + 2t -1)2t

15. (t2 _ 1)2

(t 2 + t -1)( -5/4)t- 9/4 - t-5/4(2t + 1)

16. 2 2

(t + t -1)

17. i9, y = i9t +;@ 18.!, y = !t

III, §5, Supplementary Exercises, p. 89

1. 9x 2 -

4 3. 2x + 1 5. -7. x2 -1 + (x + 5X2x)

9. + 2x)(x4 -99) + (X

3/2 + x2)(4x 3)

11. (4X{:2 + 4x + 8) + (2x

2 + 1)( + 4)

13. (x + 2Xx + 3) + (x + 1)(x + 3) + (x + lXx + 2)

15. 3x2(X

2 + 1)(x + 1) + x 3 (2x)(x + 1) + (X 3 XX 2 + 1) -2 5(3x2 + 4x) -2(x + 1) + 2x

17. 2 19. 3 2 2 21. 2

(2x + 3) (x + 2x ) (x + 1) (x + lXx -1)3(!x-

I/2) -

3XI/2[(X -1) + (x + 1)]

23. (x + 1)2(x _ 1)2

(x 2 + 1)(x + 7)(5x4) -(x 5 + 1)"x 2 + 1) + (2x)(x + 7»)

25. (x2 + 1)2(x + 7)2

(1 -x2)(3x2) -x 3( -

2x) (x

2 + 1)(2x -1) -(x2 -x)(2x)

27. (l _ X2)2 29. (x2 + 1)2

(x 2 + X -4)(2) -(2x + 1)(2x + 1)

31. ( 2 4)2

X +x- (x 2 + 2)(4 -3x2) -(4x -x 3 )(2x) -5x -(1 -5x) n 2 22 li (x + ) (x + 1)(x -2X2x) -x2"x -2) + (x + 1»)

37. 2 2

(x + 1) (x -2) (4x 3 - x 5 + 1)(12x 3 + iX'/4) -(3x4 + x5/4)(12x2 -5x4)

39. (4x3 _ x5 + 1)2

41. (y -18) = H(x -16) 43. (y + 12) = 19x 45. (y -to) = 14(x -I)

4 -12 4 -4

47. Y -9 = 81 (x -2) 49. y -3 = 9 (x -2)

51. Point of tangency: (3, -3). Both curves intersect here and have slope -1.

53. Both curves have the point (1, 3) in common and have slope 6 at this point.

55. Tangent line (y -7) = 16x at (0,7); tangent line (y -19) = 16(x -1)

at (I, 19); tangent line (y + 13) = 16(x + I) at (-I, -13).

ANSWERS TO EXERCISES

III, §6, p. 99

1. 8(x+ 1)7 2. !(2x-5)-1/2·2 3.3(sinx)2cosx 4.5(lOgX)4G)

1 1

5. (cos 2x)2 6. -2--1 (2x) 7. e

COSX ( -sin x) 8. . (r + cos x) x + eX + sm x

9. cos log x + -2 10. . 2 [

IJ(1 1) sin 2x -(x + l)(cos 2x)2

X X x

(sm 2x) 1

11. 3(2x2 + W(4x) 12. -[sin(sin 5x)](cos 5x)5 13. -2-(-sin 2x)2

cos x

14. [cos(2x + W](2(2x + 5»)(2). 15. [cos(cos(x + 1»)]( -sin(x + 1»)

1 3 1 2

16. (cos eX)e

X

17. -(3x _ 1)8 [4(3x -\) ]·3 18. -(4X)6' 3(4x) ·4

1 1

19. -(. 2)4 2(sin 2x)(cos 2x)· 2 20. -2 4 2(cos 2x)( -sin 2x)2

sm x (cos x) 1

21. (. 3 2 (cos 3x)· 3 22. -sin

2 x + cos2 x 23. (x2 + l)ex + 2xe x sm x)

24. (x3 + 2x)(cos 3x)· 3 + (3x

2 + 2) sin 3x 1 2e x cos 2x -(sin 2x)eX

25. - ( . )2 (cos X -sin x) 26.

sm x + cos x e 2x (x2 + 3)/x -(log x)(2x) cos 2x -(x + \)( -sin 2x)· 2

27. 2 2 28. 2

(x + 3) cos 2x

29. (2x -3)(e

X + \) + 2(e X + x) 30. (x3 -1)(e 3x . 3 + 5) + 3x 2 (e 3x + 5x) (x -1)3x2 -(x3 + \) (2x + 3)2x -(x2 -1)2

31. (x _ 1)2 32. (2x + W

33. 2(X

4/3 - eX) + -eX)(2x + 1)

34. (sin 3x)ix-

3/4 + 3(cos 3X)(X I/4 -

1) 35. [cos(x2 + 5x)](2x + 5)

3x' +8 -I 1 3

36. e (6x) 37. [Iog(X4 + 0]2' X4 + 1 ·4x

- 1 1 I _ 1/2 2e x - 2xe x

38. [Iog(X1/2 + 2X)]2 (x1/2 + 2x) (IX + 2) 39. e2x

2x . 4

40. -I --6' 65

. +x

III, §6, Supplementary Exercises, p. 100

I. 2(2x + 1)2 3. 7(5x + 3)65 5. 3(2x2 + X -W(4x + 1)

7. !(3x + 1)- 1/2(3) 9. -2(x

2 + X -0-3(2x + 1) 11. -i(x + 5)- 8/3

13. (x -1)3(x -W + (x -WIS. 4(x

3 + x2 -2x -1)3(3x2 + 2x -2)

17. (x -1)1/2(i)(x + 0-

1/4 -(x

+ 1)3 /4A6 ANSWERS TO EXERCISES

(3x + + X -1)3/2(4x + 1) -(2X2 + X -1)5/2(9)(3x + 2)8(3)

19. (3x+2)18

21. i(2x + 1) - 1/2(2) 23. i(x

2 + X + 5) - 1/2(2x + 1)

25. 3x2cos(X

3 + 1) 27. (e xJ 1 )(3x2) 29. (cos(cosx»)(-sinx)

31. (esin(x

J + 1l)(3x 2 cos(x3 + 1))

33. [cos"x + 1)(x2 + 2»)][(x + 1)(2x) + (x

2 + 2)]

35. (e(x+ I)(x-3»"X + 1) + (x -3» 37. 2 cos(2x + 5)

39. _ 2 _ 41. (COS x -5 )(2X + 4) -(x -5)2)

2x + 1 2x + 4 (2x + 4)2

43. (e2x2+3X+I)(4x + 3) 45. 2x 1 [cos(log2x + 1)]2

47. -(6x -2) sin(3x2 -2x + 1) 49. 80(2x + 1)79(2)

51. 49(log x )48(X -I) 53. 5( e2x + 1 - x )4(2e

2x + 1 -1)

55. !(310g(x2 + 1) -X3)- 1/2(_3_ (2x) -3x

2) 2 x 2 + 1quotesdbs_dbs10.pdfusesText_16

[PDF] Exercice page 293

[PDF] Exercice Parfum - Management Industriel et Logistique

[PDF] Exercice passif anglais - Anglais

[PDF] Exercice Pédiatrie Antibiotique - Anciens Et Réunions

[PDF] exercice phases guerre froide - Anciens Et Réunions

[PDF] Exercice physique et cancer - Divorce

[PDF] ExErcicE physiquE pEndant la grossEssE - UKK - Anciens Et Réunions

[PDF] Exercice pistolet à peinture File

[PDF] Exercice pratique 6: Explorer MSN messenger - Anciens Et Réunions

[PDF] Exercice pratique : « Insertion du fichier image Nénuphars

[PDF] Exercice preterit anglais N°3 - Anglais

[PDF] Exercice radiation adaptative

[PDF] Exercice relatif la planification

[PDF] Exercice résolu. p : 153 n°35. Tracé de vecteurs vitesse et accélération

[PDF] Exercice routage