Deck 13: Functions of Several Variables

Question 1

Describe the domain of the function

A)
B)
C)
D)
E)

Answer 1

Question 2

Sketch the surface given by the function.

A)
B)
C)
D)
E)none of the above

Answer 2

Question 3

Find and simplify for the given function

A)
B)
C)
D)
E)

Answer 3

Question 4

Find and simplify the function at the given value

A)-42
B)-14
C)42
D)14
E)

Question 5

Find and simplify the function at the given value

A)
B)
C)
D)
E)

Question 6

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)

Question 7

Find by using the limits and

A)
B)
C)
D)
E)

Question 8

Find and simplify the function at the given value

A)
B)
C)
D)
E)

Question 9

Find and simplify the function at the given value

A)
B)
C)
D)
E)

Question 10

Describe the level curves of the function.Sketch the level curves for the given c- values.

A)
B)
C)
D)
E)

Question 11

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 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

Question 12

Sketch the level curves of the function for the given c-values

A)
B)
C)
D)
E)

Question 13

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

Question 14

Describe the domain of the function

A)
B)
C)
D)
E)

Question 15

Sketch the level curves for the function for the given c-values

A)
B)
C)
D)
E)

Question 16

Sketch the surface given by the function

A)
B)
C)
D)
E)

Question 17

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)

Question 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)

Question 19

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

Question 20

Find and simplify the function at the given value

A)-56
B)-26
C)-14
D)-44
E)-27

Question 21

Find by using the limits and

A)
B)
C)
D)
E)

Question 22

Use polar coordinates to find the limit.[Hint: Let and note that implies

A) 1
B) 0
C) 2
D)
E)limit does not exist

Question 23

Find the limit .

A)
B)
C)
D)
E)

Question 24

Use spherical coordinates to find the limit [Hint: Let nd note that implies

A)6
B)9
C)1
D)7
E)

Question 25

Determine the continuity of the function

A)continuous except at
B)continuous except at
C)continuous except at
D)continuous except at
E)continuous everywhere

Question 26

Find the limit.

A)
B)
C)
D)
E)

Question 27

Find the limit or the function

A)
B)
C)
D)
E)

Question 28

Find the limit.

A)
B)
C)
D)
E)

Question 29

Use polar coordinates to find the limit [Hint: Let and note that

A)
B)
C)
D)
E)

Question 30

Determine the continuity of the composite function and

A)continuous except at
B)continuous for all
C)continuous for all
D)continuous except at
E)continuous everywhere

Question 31

Find the limit.

A)
B)
C)
D)
E)

Question 32

Find the limit.

A)
B)
C)
D)
E)

Question 33

Find the limit for the function

A)
B)
C)
D)
E)

Question 34

Use polar coordinates and L'Hopital's Rule to find the limit.

A)
B)
C)
D)
E)

Question 35

Determine the continuity of the function

A)continuous except at
B)continuous for
C)continuous except at
D)continuous except at
E)continuous for

Question 36

Determine the continuity of the function

A)continuous except at
B)continuous except at
C)continuous for all
D)continuous for all
E)continuous everywhere

Question 37

Find the limit for the function

A)
B)-6
C)
D)16x
E)6y

Question 38

Discuss the continuity of the function.

A) is continuous everywhere except at those points such that
B) is continuous everywhere except at those points such that
C) is continuous at those points
D) is continuous only when
E) is continuous everywhere in the xy-plane.

Question 39

Find the limit for the function

A)-5y
B)
C)
D)5y
E)8x

Question 40

Determine the continuity of the function

A)continuous except at
B)continuous except at
C)continuous except at
D)continuous except at
E)continuous everywhere