Question

1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value of f (m) a value of z where f is increasing but concave down (n) the equation of a vertical asymptote of f (o) the left-hand Riemann sum for f associated to the partition P (2,4,7,8) 2. The parts of this question are unrelated to one another (a) (10 pts) The efficiency of a machine at time t is given by E(t) 3-4teunits per hour. At what time between t 0 andt2 is the machine least efficient? (b) (10 pts) In the context of physics, power, measured in watts, is defined to be the instantaneous rate of doing work. If the power of a motor at time t (measured in seconds) is P(t) -4 sin t +cos 3t, find the work done by the motor from time 0 to time . Write your answer with correct units. (c) (4 pts) The graph of some unknown function f is given below, at left. Sketch, on the right-hand axes, the graph of f.

Answer 1

From iven () f(9)O → ahve chang, n ii) 71(-2) 9 24 (2)12 ニヲ.or 2ニー4 7 Rumann Sum92

2t E(t) 3-4と = -2t (t) dk 0 l4 cost 3