December 13, 2004
Math 111 C — Final Exam
Show all work clearly for partial credit. Do not use the graphing capabilities of your calculator.
1. (18 points) Find:
(a) d
dx(xln(x2+ 1)) (b) Z(sin 3x+ 2ex)dx (c) lim
x→−∞
x2
2x2+ 3x−4
2. (12 points) If f0(x) = 3x4−8x3+ 6x2, find intervals of concavity and inflection points of the
original function f.
3. (12 points) A box with an open top is required to have its length twice its
width and its volume 288 in3. What dimensions will give a minimum surface
area (not including the top)?
4. (12 points) A spotlight on the ground is trained on a parachutist who is descending vertically
toward a spot on the ground 80√3 ft away from the spotlight. When the parachutist is 80 ft
above the ground and falling at 12 ft/sec, how fast is the angle between the ground and the
beam of the spotlight decreasing, in radians per second?
5. (11 points) On a planet where the acceleration of gravity is 10 m/sec2, an astronaut stands
at the edge of a cliff and drops a rock (with initial velocity 0). The rock hits the ground at
the base of the cliff 3 sec later. How high was the cliff (in meters)?
6. (18 points) Evaluate:
(a) Zln 2
0
ex
1 + exdx (b) Z1
−1
x
9 + x4dx (c) Z√3/2
0
dx
√1−x2
7. (7 points) Use the Lefthand Rule with n= 5 to approximate the area between the curves:
