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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
