Page 332 - Calculus Demystified

Final Exam
1 319

(a) h (x) =
x cos x
x sin x
(b) h (x) =

x cos x
cos x − x sin x

(c) h (x) =
x cos x

(d) h (x) = x · sin x · ln x
x cos x

(e) h (x) =
sin x
3
30. If g(x) =[x + 4x] 53 then
3

(a) g (x) = 53 ·[x + 4x] 52
2
3

(b) g (x) = 53 ·[x + 4x] 52 · (3x + 4)
2

(c) g (x) = (3x + 4) · 53x 3
3

(d) g (x) = x · 4x
3
x + 4x

(e) g (x) =
2
2x + 1
31. Suppose that a steel ball is dropped from the top of a tall building. It takes
the ball 7 seconds to hit the ground. How tall is the building?
(a) 824 feet
(b) 720 feet
(c) 550 feet
(d) 652 feet
(e) 784 feet
2
32. The position in feet of a moving vehicle is given by 8t − 6t + 142. What
is the acceleration of the vehicle at time t = 5 seconds?
(a) 12 ft/sec 2
(b) 8 ft/sec 2
(c) −10 ft/sec 2
(d) 20 ft/sec 2
(e) 16 ft/sec 2
2
3
33. Let f(x) = x − 5x + 3x − 6. Then the graph of f is
(a) concave up on (−3, ∞) and concave down on (−∞, −3)
(b) concave up on (5, ∞) and concave down on (−∞, 5)
(c) concave up on (5/3, ∞) and concave down on (−∞, 5/3)
(d) concave up on (3/5, ∞) and concave down on (−∞, 3/5)
(e) concave up on (−∞, 5/3) and concave down on (5/3, ∞)