MAC2311_Homework_Answers

MAC2311_Homework_Answers - Answers to the Exercise Sets...

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Unformatted text preview: Answers to the Exercise Sets Exercise Set 1 1. (a) 5- π (b) 2 x + 1 (c) 1- 2 x (d) | 2 x | - x = ( x if x ≥- 3 x if x < 2. (a) x = a 2 (b) x = 1 (c) x = 1 / 3 (d) x = ± q 3 2 3. (a) [- 1 , 0] ∪ [5 , ∞ ) (b)- 1 , 3 2 (c) (-∞ ,- 7 2 ) ∪ ( 1 2 , ∞ ) (d) ( , 2 3 (e) (-∞ ,- 1) ∪ - 1 3 , 1 (f) (-∞ ,- 1 2 ∪ ( 1 5 , ∞ ) 4. 5 5. (1 ,- 3) and (- 5 ,- 3) 6. y =- 2 3 x- 7 3 7. y = 2 5 x- 16 5 8.- 3 3 9 x y 9. (a) center (0 , 0), radius 7, x-intercepts ± 7, y-intercepts ± 7 (b) center (3 ,- 2), radius 5, x-intercepts 3 ± √ 21, y-intercepts- 6 and 2 10. (a) y = (2 . 2%) t + 5 . 4% (b) 9.8% 11. (b) 5 ≤ C ≤ 45 12. [2 , 3] (in seconds) 13. 11 . 98 ≤ x ≤ 12 . 02 (in inches); Area ∈ [143 . 5204 , 144 . 4804] (in square inches) Exercise Set 2 1. (a) 10 π/ 3 (b)- 105 ◦ 2. (a) 16 π 3 cm (b) 64 π 3 cm 2 3. (a)- 540 ◦ ◦ 90 ◦ (b) 10 π 3 ◦ 90 ◦ 4. (a) sin (- 5 π 2 ) =- 1, cos (- 5 π 2 ) = 0, tan (- 5 π 2 ) does not exist, csc (- 5 π 2 ) =- 1, sec (- 5 π 2 ) does not exist, cot (- 5 π 2 ) = 0 (b) sin ( 11 π 6 ) =- 1 2 , cos ( 11 π 6 ) = √ 3 2 , tan ( 11 π 6 ) =- 1 √ 3 , csc ( 11 π 6 ) =- 2, sec ( 11 π 6 ) = 2 √ 3 , cot ( 11 π 6 ) =- √ 3 5. cos θ =- 2 3 , sin θ =- √ 5 3 , tan θ = √ 5 2 , csc θ =- 3 √ 5 , cot θ = 2 √ 5 6. 9.8506 in 7. (a) true (b) false (c) true 8. (a) 7/25 (b) 6 5 √ 13 10. π/ 3, 5 π/ 6 11. (a) 0, π/ 4, π , 7 π/ 4 (b) π/ 6, 5 π/ 6, 3 π/ 2 (c) π/ 4, 5 π/ 4 (d) π/ 4, 3 π/ 4, 5 π/ 4, 7 π/ 4 12. (a) , π 3 ∪ 2 π 3 , 2 π ) (b) , π 4 ) ∪ ( 5 π 4 , 2 π ) 13. π 2 ,π ) ∪ 3 π 2 , 2 π ) 14. (b) θ = π/ 3, A = 27 √ 3 in 2 Exercise Set 3 1. (a) 5 (b) x ∈ { 5 , 8 } (c) domain [0 , 10], range [- 2 , 5] (d) true 2. (a) no (b) yes (c) yes (d) no 3. (a) Temperature Time (hours) (b) Score Time (hours) (c) D Hand Position 4. Volume(gallons) Time (minutes) 5. (a) x 2- 1 x 2 + 1 (b) 2 a 2 a + 2 (c) 2 h 9 + 3 h (d) 2 ( a + 1)( a + h + 1) 6. 3 s 2 + 3 s + 1 7. (a) 3 2 , ∞ ) (b) (-∞ , 0) ∪ (0 , ∞ ) (c) (-∞ ,- 1) ∪ (- 1 , ∞ ) (d) [0 , 1) ∪ (1 , ∞ ) (e) (-∞ , 0) ∪ [1 , ∞ ) 8. (b) f ( x ) = ( 2 if x > if x < 2 x y (c) f ( x ) = 1- x , x 6 =- 1 1 1 (- 1 , 2) x y 9. If A is the area of the pen in square feet, then A ( x ) = x (500- 2 x ) with domain [0 , 250]. 10. If V is the volume of the can in cubic centimeters, then V ( r ) = 1 2 r (100- 2 πr 2 ) with domain , p 50 /π i . 11. If S is the surface area of the can in square centimeters, then S ( r ) = 2 π r 2 + 1000 r with domain (0 , ∞ ). 12. (a) (b) 13. f ( x ) Power? Poly.? Alg.? Trans.? x 2 X X X x 2 / 3 X X e x X x e X X x x X Exercise Set 4 1. (a) Shift left 2 units, then reflect across the y-axis. Reversing these steps instead yields the graph of f (- 2- x )....
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MAC2311_Homework_Answers - Answers to the Exercise Sets...

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