Question 1

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

Accepted Answer

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

Question 2

Determine the continuity of the function

Accepted Answer

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

Question 3

Find  by using the limits  and

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Find and simplify  for the given function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Describe the domain of the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

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.

Accepted Answer

A) $5,148.94 
B) $3,319.05 
C) $2,493.01 
D) $2,479.09 
E) $4,219.43

Question 7

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.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Sketch the surface given by the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

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.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

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.

Accepted Answer

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 11

Find the limit  or the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Describe the domain of the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Find and simplify the function  at the given value

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

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.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Find  by using the limits  and

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Discuss the continuity of the function.

Accepted Answer

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 17

Find the limit  for the function

Accepted Answer

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

Question 18

Find and simplify the function  at the given value

Accepted Answer

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

Question 19

Find the limit.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Find the limit .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 13: Functions of Several Variables

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

Determine the continuity of the function

Find by using the limits and

Find and simplify for the given function

Describe the domain of the function

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.

Sketch the surface given by the function

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.

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.

Find the limit or the function

Describe the domain of the function

Find and simplify the function at the given value

Find by using the limits and

Discuss the continuity of the function.

Find the limit for the function

Find and simplify the function at the given value

Find the limit.

Find the limit .