Review Exercises AN11 9. (a) ( ) = − A x x x 4 4 2 (b) ( ) = + − p x x x 4 4 4 2 (c) A is largest when ≈ x 1.41. 0 10 2 0 (d) p is largest when ≈ x 1.41. 0 12 2 0 11. (a) π ( ) = + − + A x x x x 25 20 4 2 2 (b) Domain: { } < < x x 0 2.5 (c) A is smallest when ≈ x 1.40 m. 8 0 0 2.5 2.6 Assess Your Understanding (page 128) 1. (a) ( ) = − + d x x x 15 64 4 2 (b) ( ) = d 0 8 (c) ( ) = ≈ d 1 50 7.07 (d) 40 210 25 10 (e) d is smallest when ≈ − x 2.74 or ≈ x 2.74 3. (a) ( ) = − + d x x x 1 2 (b) 0 2 2 0 (c) d is smallest when = x 0.5. (d) ≈ 3 2 0.87 5. ( ) = A x x 1 2 4 7. (a) ( ) ( ) = − A x x x 16 2 (b) Domain: { } < < x x 0 4 (c) The area is largest when ≈ x 2.31. 0 30 4 0 (d) The largest area is approximately 24.63 square units. 13. (a) ( ) = C x x (b) π ( ) = A x x 4 2 15. (a) ( ) = A r r2 2 (b) ( ) = p r r6 17. π ( ) = − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ A x x 3 3 4 2 19. (a) ( ) = − + d t t t 2500 360 13 2 (b) d is smallest when ≈ t 0.07 hr. 0 5 0.2 0 21. π ( ) ( ) = − V r H R r r R 2 23. (a) ( ) = − + + T x x x 12 5 4 3 2 (b) { } ≤ ≤ x x 0 12 (c) 3.09 hr (d) 3.55 hr 25. (a) ( ) ( ) = − V x x x 24 2 2 (b) 972 in.3 (c) 160 in.3 (d) V is largest when = x 4 in. 0 1100 12 0 (e) The largest volume is 1024 in.3 27. (a) ( ) = + + C x x x 9000 1.60 2910 (b) The retailer should order 75 drives per order for a minimum yearly cost of $3150. 28. { } 0, 3 29. 64 mi h 30. = − m 4 31. 5.6 32. = − y u u 1 33. +x x 4 5 3 2 3 34. ∅ 35. ( ) −3, 2 36. = P t E v d 6.76 2 2 4 37. 97 Review Exercises (page 133) 1. (a) Domain: { } 8, 16, 20, 24 ; range: { } $6.30, $12.32, $13.99 (b) ( ) ( ) ( ) ( ) { } 8, $6.30 , 16, $13.99 , 20, $12.32 , 24, $13.99 (d) (20, 12.32) y x 10 20 10 20 (16, 13.99) (24, 13.99) (8, 6.30) 2. Domain: { } −1, 2, 4 ; range: { } 0, 3 ; function 3. Domain: { } 2, 4 ; range: { } −1, 1, 2 ; not a function 4. Domain: [ ] −1, 3 ; range: [ ] −2, 2 ; not a function 5. Domain: all real numbers; range: [ ) − ∞3, ; function 6. (a) 2 (b) −2 (c) − − x x 3 1 2 (d) − − x x 3 1 2 (e) ( ) − − + x x x 3 2 4 3 2 (f) − x x 6 4 1 2 7. (a) 0 (b) 0 (c) − x 4 2 (d) − − x 4 2 (e) − x x4 2 (f) − x 2 1 2 8. (a) 0 (b) 0 (c) − x x 4 2 2 (d) − − x x 4 2 2 (e) ( ) ( ) − − x x x 4 2 2 (f) − x x 1 2 2 9. { } ≠ − ≠ x x x 3, 3 10. { } ≤ x x 2 11. { } ≠ x x 0 12. { } ≠ − ≠ x x x 3, 1 13. [ ) ( ) − ∪ ∞ 1, 2 2, 14. { } > − x x 8 15. ( )( ) + = + f g x x2 3; Domain: all real numbers ( )( ) − = − + f g x x4 1; Domain: all real numbers ( )( ) ⋅ = − + + f g x x x 3 5 2; 2 Domain: all real numbers ( ) ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = − + f g x x x 2 3 1 ; Domain: { } ≠ − x x 1 3 (c) 8 Batteries, x 16 24 20 $6.30 $12.32 $13.99 Price, y 16. ( )( ) + = + + f g x x x 3 4 1; 2 Domain: all real numbers ( )( ) − = − + f g x x x 3 2 1; 2 Domain: all real numbers ( )( ) ⋅ = + + f g x x x x 9 3 3 ; 3 2 Domain: all real numbers ( ) ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ = + + f g x x x x 3 1 3 ; 2 Domain: { } ≠ x x 0
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