advertisement

c Math 151 WIR, Spring 2010, Benjamin Aurispa Math 151 Exam 1 Night Before Drill Answer Key 3 1. (a) f 0 (x) = √ 2 3x + 7 (b) y − 4 = 38 (x − 3) OR y = 38 x + 23 8 2. < 14, 2 > 3. (a) (b) 3 28 ft/sec 3 f 0 (3) = 25 ft/sec ( x2 − 4 if x ≤ −2, x ≥ 2 2 −(x − 4) if − 2 < x < 2 See Full Solutions for a graph. Not differentiable at x = −2 and x = 2 4. f (x) = − 4| = 8 5 √ ,√ 89 89 10 8 √ ,√ 41 41 5. 6. |x2 D √ √ √ E 7. True velocity vector of plane: 150 3 + 10 2, 150 − 10 2 q √ √ √ Groundspeed = (150 3 + 10 2)2 + (150 − 10 2)2 8. F =< 4, 5 >; |F| = √ 41; θ = arctan 5 4 (where θ is the angle formed with the positive x-axis) 9. Scalar Projection: − √55 ; Vector Projection: < −2, −1 > 10. arccos √ −24 √ 34 40 11. 120 J 12. Cartesian equation: x2 + (y − 1)2 = 9; Curve is a circle of radius 3 centered at (0, 1). Direction of motion as t increases is counterclockwise. 13. x = 8 − 4t, y = 1 + 4t √ √ 14. a = 10, − 10 15. (a) 2 3 (b) −∞ (c) ∞ (d) 0 (e) D 8 6, 13 E (f) −4 (g) DNE: lim f (x) = −9 whereas lim f (x) = 9 x→3− (h) x→3+ 5 2 16. Vertical Asymptote: x = 17 ; Horizontal Asymptote: y = 1 6 7 c Math 151 WIR, Spring 2010, Benjamin Aurispa 17. Using the Intermediate Value Theorem, there are solutions on the interval (−2, −1) and on the interval (1, 2). 18. f (x) is not continuous at x = 1 since lim f (x) = 10, but f (1) = 5. x→1 f (x) is also not continuous at x = 3 since lim f (x) DNE. x→3 19. No value of m will make f continuous everywhere. 2