Unit 5 Answers

5-1 Answers

1. First = 10 Second = 10

2. l = 9 cm w = 9 cm

3. l = 20 ft w = 20 ft

4. x = 30 ft y = 40 ft

5. x = 9 ft y = 6 ft

6. x = 2 in

7.(3, 32)

8. See picture below:

9.dV

dt= 324π in3/min

10.dx

dt= 375 mi/hr

11. (a) DNE

(b) 2

(c) ∞(d) 1

(e) 1

(f) x = 0, 4, 5

(g) x = 5

(h) 4

(i) 0

(j) −1(k) 0

(l) x = 0, 2, 4, 5 (maybe 3?)

(m) x = 0, 2

(n) none

5-2 Answers

1. First = 30 Second = 10

2. First = 2412 Second = 1

2

3. x = 0 y = 25

4. 400 m by 800 m

5. x = .6068 ft

6. V = 4.104 ft3

7.(√

18,√18)

8. A = 36

9. x = 20 cm by y = 10 cm

10. See picture below:

11. See picture below:

12.dy

dx=−6x+ 6

(x2 − 2x)4

13. f ′(x) = 12 (x

3 − 3x+ 2)−12 (3x2 − 3)

14. g′(x) =1

(2x+ 3)2

15. See picture below:

16. See picture below:

17. See picture below:

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5-3 Answers

1. (a) y = −3x+ 6

(b) f(1.1) ≈ 2.7

(c) f(1.1) = 2.669

2. (a) Just Draw It

(b) y = 2(x− 1) + 1

(c) Label it

(d) f(.9) ≈ .8(e) f(.9) = .81

(f) f(.6) ≈ .2 f(.6) = .36

3. Use y =√x and (25, 5). Then

√26 ≈ 5.1

4. f(3.1) ≈ −9(3.1− 3) + 30

5. The actual value cannot be found, because the heightof the curve y = f(x) is not known.

6. When x = 5 15 , y ≈ 10.25(5 1

5 − 5) + 20

7. (a) A ≈ 65 in2

(b) A ≈ 63 in2

(c) [63, 65] in2

8. f(8.01) ≈ 112 (8.01− 8) + 2

9. y ≈ −533 (1.1− 1) + 2

10. y = 1.983 (or 1.984)

11. (a) (2 16 )

3 ≈ 12(2 16 − 2) + 8

(b) (2 16 )

3 = 10.171

12. min= −4 max= 94

13. First = 1 Second = 1

14. (a) 2389 (or 2390) people

(b) 481.009 people per day

(c) x = 9.210 Think about what this representsy = 500 Think about what this represents

(d) 2000 people

(e) Try to explain it!

(f) x = 6.576 days

15. max A = 180000 yd2

16. See picture below:

17. See picture below:

18. See picture below:

19. (0,−6) (4,−62)

20. No relative extrema

21. 15

22. 0

23. c = −1.190 (or −1.191)

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5-4 Answers

1.−12x2

+ C

2. 45 t

54 + C

3. 13x

3 − 12x

2 − 2x+ C

4. 43y

32 + C

5. 12x

4 − 13x

3 + x+ C

6.−13x

+ C

7.−19x

+ C

8. 3y − 57y

75 + C

9. 4x54 − 3x

13 + C

10. 3t3 − 30t2 + 100t+ C

11. 43x

3 − x− 12x−1 + C

12. 2t− 2t12 + C

13. 27y

72 + y2 + C

14. x3 − 2x2 + 2x− 4

15. y =3

t+ t+ 6

16. (a) y = 2x32 + C

(b) y = 2x32 − 16

17. g(x) = 13x

3 − 32x

2 − 5x− 76

18. (2x− 1)3

19. (a) v(t) = 3t2 − 4t+ 5

(b) v(2) = 9

(c) s(t) = t3 − 2t2 + 5t− 2

(d) s(2) = 8

20. (a) a(t) =1

2√t

(b) a(9) = 16

(c) s(t) = 23 t

32 + t− 7

21. t =√10 sec.

22. (a) v(t) =

{3t, 0 < t ≤ 4

12, t > 4

(b) v(2) = 6 m/sec v(4) = 12 m/sec v(6) =12 m/sec

(c) s(t) =

{32 t

2, 0 < t ≤ 4

12t− 24, t > 4

(d) 24 m

(e) 10.333 sec

23. See picture below:

24. See picture below:

25. See picture below:

26. f−1(x) = 8x3 + 3

27. y − 4 = 13 (x− 8)

28. d = 2 c = 0 a = −2 b = −6

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5-5 Answers

1.(3x− 2)6

6+ C

2. 145 (5t− 3)9 + C

3. −23√4− x3 + C

4. 13 (y

2 − 3)32 + C

5. − 1

3(x3 + 2)5+ C

6. 6√1− v + C

7.(2x2 − 3x)5

5+ C

8. −116 (2x2 − 4x)−4 + C

9. 211 (√t− 4)11 + C

10. 310 (5x)

23 + C =

3

2 3√5x

23 + C

11. 43u

3 + 2u2 + u+ C = 16 (2u+ 1)3 + C

12. 15y

5 − 13y

3 + C

13. x+ 3x + C

14. 65x

52 + 2

3x32 − 4x

12 + C

15. 45 (x+ 1)

52 − 4

3 (x+ 1)32 + C

16. 3√2x− 1− 2

3 (√2x− 1)3 + C

17. −43 (1− x) 32 − 2

5 (1− x)52 + C

18. −92 x23 + 3x− 71

2

19. (x2 − 3)4

20. (a) a(t) = 29 t−

23

(b) y(t) =(13 t− 1

)3+ C

(c) t = 3

(d) (−∞, 3) , (3,∞)

(e) always

(f) 8

(g) (3,∞)

21. TL: y − 1 = 32 (x− 2)

NL: y − 1 = −23 (x− 2)

22. f ′(1) = 14

23. 13

24. (a) Problem 23 (ARC)

(b) Problem 22 (IRC)

25. c = .732

26. (a) (0, 0), (0, 4)

(b) (±√2, 2)

27. f(2.1) ≈ 9(2.1− 2) + 7

28. See below

29. (a) 2

(b) 3

(c) −2(d) −2(e) −∞(f) DNE

(g) 0

(h) DNE

30. You know the answer, show your work.

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5-6 Answers

1. 3

2. −π

3. 2− 2π

4. 8− 2π

5. (a) −4(b) 5

6. (a) 2

(b) 52

7. −2

8. 8

9. 110

10. −6 12

11. 4

12. 23110

13. 13

14. 163

15. 3328

16. (a) 3

(b) −3(c) 6

(d) −3

17. (a) 5

(b) 0

(c) 0

(d) −5

18. 2.484 (or 2.485)

19. 36.547

20. (a) 1.098 (or 1.099)

(b) 4.098 (or 4.099)

21. 16.535 (or 16.536)

22. (a) v(t) = 3t2 − 6t

(b) 6t− 6

(c) −3(d) 3

(e) t < 1

(f) 18

(g) 22

(h) 18

(i) 22.000

23. 8.656

24. (a) Do: all reals no V.A. H.A.: y = 0x-int: (0, 0) odd y-int: (0, 0) origin symme-try

(b) rel. max: x = 1 rel. min: x = −1(c) P.I. at x = 0,±

√3

(d) See Below

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5-7 Answers

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