Stewart – Calculus ET 8e Chapter 14 Form D
____ 8. If R is the total resistance of three resistors, connected in parallel, with resistances , then
.
If the resistances are measured in ohms as , with a possible error
of 0.8% in each case, estimate the maximum error in the calculated value of R.
a. 0.347
b. 0.476
c. 0.291
d. 0.098
e. 0.957
____ 9. Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8
cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01
cm thick. (rounded to the nearest hundredth.)
a. 8.34
b. 6.99
c. 6.91
d. 6.7
e.
____ 10. A boundary stripe 2 in. wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.
Use differentials to approximate the number of square feet of paint in the stripe.
a. 113
b. 113.81
c. 113.22
d. 113.89
e. 113.33
Stewart – Calculus ET 8e Chapter 14 Form D
____ 11. Use the Chain Rule to find .
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 14 Form D
____ 12. Use the Chain Rule to find .
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 14 Form D
____ 13. Use the Chain Rule to find
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 14 Form D
____ 14. Use the equation to find .
a.
b.
c.
d.
e.
____ 15. Find the directional derivative of at the point (1, 3) in the direction toward the
point (3, 1).
Select the correct answer.
a.
b.
c.
d. 28
e. none of these
Stewart – Calculus ET 8e Chapter 14 Form D
____ 16. Find equations for the tangent plane and the normal line to the surface with equation
at the point
a. ,
b. ,
c. ,
d. ,
____ 17. If use the gradient vector to find the tangent line to the level curve
at the point .
a.
b.
c.
d.
e.
____ 18. Find and classify the relative extrema and saddle points of the function
for and .
a. None
b. Relative maximum
c. Saddle point
d. Relative minimum
Stewart – Calculus ET 8e Chapter 14 Form D
____ 19. At what point is the following function a local maximum?
a.
b.
c.
d.
e.
____ 20. Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 14 Form D
Answer Key
Stewart – Calculus ET 8e Chapter 14 Form E
____ 1. Let Find
Select the correct answer.
a.
b.
c.
d.
____ 2. Let Find
Select the correct answer.
a.
9
10
b.
45
2
c. 225
d.
3. Evaluate the limit.
4. Evaluate the limit.
5. Find the limit Hint: If and then if
and only if
6. Determine where the function is continuous.
Stewart – Calculus ET 8e Chapter 14 Form E
____ 7. Find for .
Select the correct answer.
a. 0
b.
c.
d.
e.
8. How many nth-order partial derivatives does a function of two variables have?
9. Use the definition of partial derivatives as limits to find if .
____ 10. Find for the function
Select the correct answer.
a.
b.
c.
d.
11. A boundary stripe 2 in. wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.
Use differentials to approximate the number of square feet of paint in the stripe.
12. Use the Chain Rule to find .
Stewart – Calculus ET 8e Chapter 14 Form E
13. Use the equation to find .
14. Find equations for the tangent plane and the normal line to the surface with equation
at the point
15. Find the gradient of the function .
____ 16. If use the gradient vector to find the tangent line to the level curve
at the point . Select the correct answer.
a.
b.
c.
d.
e.
17. Find all the saddle points of the function.
18. Find the dimensions of the rectangular box with largest volume if the total surface area is given as
.
____ 19. Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its
12 edges is . Select the correct answer.
a. 32, 32, 32
b. 32, , 16
c. , ,
d. , ,
e. 4, 8, 16
Stewart – Calculus ET 8e Chapter 14 Form E
20. Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.
Stewart – Calculus ET 8e Chapter 14 Form E
Answer Key
Stewart – Calculus ET 8e Chapter 14 Form F
____ 1. Let Find
Select the correct answer.
a.
2
3
b.
c. 36
d.
6
2. Find the domain and range of the function .
3. Evaluate the limit.
4. Evaluate the limit.
____ 5. Find for .
Select the correct answer.
a.
b.
c.
d.
e. 0
6. Use the definition of partial derivatives as limits to find if .
Stewart – Calculus ET 8e Chapter 14 Form F
7. The height of a hill (in feet) is given by
where x is the distance (in miles) east and y is the distance (in miles) north of your cabin. If you are
at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the
height of the hill (a) in a northerly direction and (b) in an easterly direction?
8. Find the differential of the function
____ 9. Use the Chain Rule to find
Select the correct answer.
a.
b.
c.
d.
10. The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a
rate of 3.6 in/s. At what rate is the volume of the cone changing when the radius is in. and the
height is in.?
11. Use the equation to find .
12. Find equations for the tangent plane and the normal line to the surface with equation
at the point