Deck 13: Introduction to Functions of Several Variables

Question 1

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

Answer 1

B

Question 2

Answer 2

C

Question 3

and simplify the function

Answer 3

C

Question 4

Sketch the level curves of the function

Question 5

and simplify the function

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

Question 6

and simplify the function

Question 7

According to the Ideal Gas Law, 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.

Question 8

average length of time that a customer waits in line for service is

Question 9

the limit.

Question 10

Question 11

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

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 12

and simplify

Question 13

Sketch the level curves for the function

Question 14

Sketch the surface given by the function.

Question 15

Determine the continuity of the function

Question 16

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

Question 17

and simplify the function

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

Question 18

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.

Question 19

According to the Ideal Gas Law, 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.

Question 20

and simplify the function

Question 21

the partial derivative

Question 22

Question 23

Question 24

Find the limit

Question 25

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

Question 26

the partial derivative

Question 27

Question 28

the partial derivative

Question 29

the limit.

Question 30

Discuss the continuity of the function.

Question 31

Determine the continuity of the composite function

Question 32

Determine the continuity of the function

Question 33

Question 34

Determine the continuity of the function

Question 35

Question 36

the limit .

Question 37

the limit.

Question 38

Determine the continuity of the function

Question 39

the partial derivative

Question 40

Question 41

Question 42

Question 43

Suppose the temperature at any point

Question 44

Question 45

Question 46

the total differential for the function

Question 47

the partial derivative

Question 48

Find the total differential for the function

Question 49

Suppose a pharmaceutical corporation has two plants that produce the same over-the-counter medicine. If respectively, then the total revenue for the product is given by

Question 50

Question 51

the total differential of the function

Question 52

the partial derivative

Question 53

Question 54

the total differential of the function

Question 55

the first partial derivative for the function respect to z.

Question 56

simultaneously.

Question 57

Suppose the utility function derived by a person from the consumption of two products x and y. Determine the marginal utility of

Question 58

Suppose the utility function derived by a person from the consumption of two products x and y. Determine the marginal utility of product if the utility function is

Question 59

Suppose a company manufactures two types of wood-burning stoves: a freestanding model and a fireplace-insert model. The cost function for producing x freestanding and y
Fireplace-insert stoves is

Question 60

Find the partial derivative

Question 61

Question 62

towards

A)10.96
B)-6.04
C)49.96
D)31.92
E)33.92

Question 63

Question 64

Question 65

parametric equations for the paths of two projectiles are given below. At what rate is the distance between the two objects changing at places.

Question 66

Suppose the centripetal acceleration of a particle moving in a circle is

Question 67

Suppose the formula for wind chill C (in degrees Fahrenheit) is given by

Question 68

Question 69

Round your answer to four decimal places.

A)-7.9441
B)-45.9441
C)-19.9441
D)0.1118
E)-4.8882

Question 70

Question 71

Question 72

Suppose the period T of a pendulum of length L is acceleration due to gravity. A pendulum is moved from the Canal Zone, where second per second, to Greenland, where feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.6 feet to 2.45 feet. Approximate the
Change in the period of the pendulum. Round your answer to four decimal places.

A)5.8508 seconds
B)-0.0746 second
C)0.9254 second
D)7.9254 seconds
E)-7.1492 seconds

Question 73

radius r and height h of a right circular cylinder are measured with possible errors of 5% and 1%, respectively. Approximate the maximum possible percent error in measuring
The volume.

A)18 %
B)11 %
C)24 %
D)12 %
E)7 %

Question 74

Question 75

A)116t
B)58t
C)104t
D)32t
E)174t

Question 76

Suppose the formula for wind chill C (in degrees Fahrenheit) is given by

Question 77

Question 78

towards . Round your answer to four decimal places.

A)-35.7266
B)30.5500
C)17.2734
D)15.5468
E)-4.7266

Question 79

Suppose electrical power P is given by resistance. Approximate the maximum percent error in calculating the power if 140 volts are applied to a 3000-ohm resistor and the possible percent errors in measuring E and R are 5% and 8%,
Respectively.

A)24%
B)42%
C)38%
D)43%
E)18%

Question 80

Round your answer to four decimal places.

A)7.3037
B)5.6074
C)-16.6963
D)-2.6963
E)-21.3926