740 Chapter 13: Functions of Several Variables
13.1 Introduction to Functions of Several Variables
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 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.
13.1 Introduction to Functions of Several Variables 741
____ 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.
742 Chapter 13: Functions of Several Variables
____ 9. Sketch the surface given by the function .
a. d.
b. e.
c.
13.1 Introduction to Functions of Several Variables 743
____ 10. Sketch the surface given by the function.
a. d.
b. e. none of the above
c.
744 Chapter 13: Functions of Several Variables
____ 11. Describe the level curves of the function. Sketch the level curves for the given c–
values.
a. d.
b. e.
c.
13.1 Introduction to Functions of Several Variables 745
____ 12. Sketch the level curves of the function for the given c-values
.
a. d.
b. e.
c.
746 Chapter 13: Functions of Several Variables
____ 13. Sketch the level curves for the function for the given c-values
.
a. d.
b. e.
c.
13.1 Introduction to Functions of Several Variables 747
____ 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.
748 Chapter 13: Functions of Several Variables
____ 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.
13.1 Introduction to Functions of Several Variables 749
13.1 Introduction to Functions of Several Variables
Answer Section
MULTIPLE CHOICE