Larson_Calculus_10e ch13sec01
MULTIPLE CHOICE
1. Find and simplify the function at the given value .
a.
–56
b.
–26
c.
–14
d.
–44
e.
–27
2. Find and simplify the function at the given value .
a.
b.
c.
d.
e.
3. Find and simplify the function at the given value .
a.
b.
c.
d.
e.
4. Find and simplify the function at the given value .
a.
–42
b.
–14
c.
42
d.
14
e.
5. Find and simplify the function at the given value .
a.
b.
c.
d.
e.
6. Find and simplify for the given function .
a.
b.
c.
d.
e.
7. Describe the domain of the function .
a.
b.
c.
d.
e.
8. Describe the domain of the function .
a.
b.
c.
d.
e.
9. Sketch the surface given by the function .
a.
d.
b.
e.
c.
10. Sketch the surface given by the function.
a.
d.
b.
e.
none of the above
c.
11. Describe the level curves of the function. Sketch the level curves for the given c-values.
a.
d.
b.
e.
c.
12. Sketch the level curves of the function for the given c-values .
a.
d.
b.
e.
c.
13. Sketch the level curves for the function for the given c-values .
a.
d.
b.
e.
c.
14. Assume in 2009, an investment of $2400 was made in a bond earning 9% compounded annually.
Assume that the buyer pays at rate R and the annual rate of inflation is I. Suppose in the year 2019, the
value V of the investment in constant 2009 dollars is . Calculate
the function for and . Round your answer to the nearest cent.
a.
$5,148.94
b.
$3,319.05
c.
$2,493.01
d.
$2,479.09
e.
$4,219.43
15. Assume a rule that is one of several methods used to determine the lumber yield of a log (in board–
feet) in terms of its diameter d (in inches) and its length L (in feet). The number of board-feet is
. Find the number of board-feet of lumber in a log 28 inches in diameter and
feet in length.
a.
7,290 board-feet
b.
1,690 board-feet
c.
270 board-feet
d.
3,380 board-feet
e.
6,760 board-feet
16. The average length of time that a customer waits in line for service is where y
is the average arrival rate, written as the number of customers per unit of time, and x is the average
service rate, written in the same units. Evaluate . Note: x and y are given as the number of
customers per hour.
a.
7 min
b.
5 min
c.
3 min
d.
4 min
e.
6 min
17. A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z feet. It
costs $2.10 per square foot to build the base and $0.75 per square foot to build the sides. Write the cost
C of constructing the box as a function of x, y, and z.
a.
b.
c.
d.
e.
18. According to the Ideal Gas Law, , where P is pressure, V is volume, T is temperature (in
Kelvins), and k is a constant of proportionality. A tank contains 2000 cubic inches of nitrogen at a
pressure of 26 pounds per square inch and a temperature of 600 K. Determine k.
a.
b.
c.
d.
e.
19. According to the Ideal Gas Law, where P is pressure, V is volume, T is temperature (in
Kelvins), and k is a constant of proportionality. A tank contains 3500 cubic inches of nitrogen at a
pressure of 34 pounds per square inch and a temperature of 300 K. Write P as a function of V and T
after evaluating k.
a.
b.
c.
d.
e.