Review problems for Chapter 5 and Chapter 6
1. Suppose the rate at which a filter removes sediment from a tank is given by the data
below:
Rate of sediment
removal (grams/hr)
3.5
8.2
9.0
7.5
5.3
Time (hr)
0
1
2
3
4
Find the upper and lower estimates for the amount of sediment removed during the
first 4 hours.
2. An object travels back and forth in a tunnel with the given velocity function. Assume
the object started at the center of the tunnel and positive velocity indicates motion to
the right. Describe the motion of the object. Include information about time,
direction and distance traveled. Include the times that the object is in the middle of
the tunnel and explain your answers.
3
1.5
ft/sec
0
0
2
4
6
-1.5
-3
sec
8
10
3. Use the Fundamental Theorem of Calculus to find

9
1
(3 x  5)dx .
4. A. Estimate the area of the region bounded by f (x) , the x-axis, x = -4, and x = 4.
Include an illustration of f (x ). f ( x) 
1
2
e
 x2
2
. B. Estimate the average value of
f (x ) over the interval [-4, 4].
5. Sketch the graph of f ( x)  sin ( x 2 ) over the interval [0, 2]. Suppose F (x) is a
function such that F ( x)  f ( x). Describe F (x) over this interval. Include
information about where this function is increasing/decreasing, concave up/concave
down, and find all local extrema and inflection points exactly if possible (the
dependent value must be included in these points). Include a sketch of F (x) given
that F (0)  0. .