Question 1

Identify any extrema of the function  by recognizing its given form or its form after completing the square.
A) relative maximum: 
B) relative minimum: 
C) relative minimum: 
D) relative maximum: 
E) relative maximum:

Accepted Answer

The answer of Identify any extrema of the function ...

Question 2

Find the gradient of the function at the given point. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the gradient of the function at...

Question 3

Find the limit. 
A) 1
B) 
C) 
D) 
E) 0

Accepted Answer

The answer of Find the limit. 
A) 1
B) 
C) 
D)...

Question 4

Find symmetric equations of the tangent line to the curve of intersection of the surfaces  ,  at the point  . ​
A)  ​
B)  ​
C)  ​
D)  ​
E)  ​

Accepted Answer

The answer of Find symmetric equations of the tangent line...

Question 5

Describe the level curves of the function. Sketch the level curves for the given c-values. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Describe the level curves of the function....

Question 6

Suppose the period T of a pendulum of length L is  where g is the acceleration due to gravity. A pendulum is moved from the Canal Zone, where  feet per second per second, to Greenland, where  feet per second per second. Because of the change in temperature, the length of the pendulum changes from 2.5 feet to 2.43 feet. Approximate the change in the period of the pendulum. Round your answer to four decimal places. ​
A) 4.9300 seconds
B) -0.0350 second
C) 0.9650 second
D) 7.9650 seconds
E) -1.0700 seconds

Accepted Answer

The answer of Suppose the period T of a pendulum...

Question 7

Find a unit normal vector to the surface  at the point  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a unit normal vector to the...

Question 8

Find the limit  for the function  . ​
A) 2x
B) -4
C) 0
D) 4x
E) 4y

Accepted Answer

The answer of Find the limit  for the function...

Question 9

Find the maximum value of the directional derivative at the point  of the function  . Round your answer to two decimal places. ​
A) 193.87
B) 252.00
C) 262.08
D) 283.46
E) 230.51

Accepted Answer

The answer of Find the maximum value of the directional...

Question 10

Find the absolute extrema of  on the region bounded by the square with vertices  and  . ​
A) absolute minimum: 
Absolute maximum: 
​
B) absolute minimum: 
Absolute maximum: 
​
C) absolute minimum: 
Absolute maximum: 
​
D) absolute minimum: 
Absolute maximum: 
​
E) absolute minimum: 
Absolute maximum: 
​

Accepted Answer

The answer of Find the absolute extrema of  on...

Question 11

Find the critical points of the function  , and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.
A) relative minimum at 
B) relative maximum at 
C) relative maximum at 
D) relative minimum at 
E) no relative extrema

Accepted Answer

The answer of Find the critical points of the function...

Question 12

Find a unit normal vector to the surface  at the point  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a unit normal vector to the...

Question 13

Find  for function  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find  for function  .
A) 
B)...

Question 14

Use Lagrange multipliers to find the maximum value of  where  and  subject to the constraint  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use Lagrange multipliers to find the maximum...

Question 15

Find  using the appropriate Chain Rule for  where  , and  . ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find  using the appropriate Chain Rule...

Question 16

Find the partial derivative  for the function  . ​
A)  ​
B)  ​
C)  ​
D)  ​
E)  ​

Accepted Answer

The answer of Find the partial derivative  for the...

Question 17

Use Lagrange multipliers to find the minimum distance from the parabola  to the point  . Round your answer to two decimal places. ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use Lagrange multipliers to find the minimum...

Question 18

Find the angle of inclination  of the tangent plane to the surface  at the point  . Round your answer to two decimal places.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the angle of inclination  of...

Question 19

​Find the partial derivative  for the function  . ​
A)  ​
B)  ​
C)  ​
D)  ​
E)  ​

Accepted Answer

The answer of ​Find the partial derivative  for the...

Question 20

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function  at the critical point  , if  . ​
A) relative maximum
B) relative minimum
C) saddle point
D) insufficient information

Accepted Answer

The answer of Determine whether there is a relative maximum,...

Quiz 13: Functions of Several Variables

Identify any extrema of the function by recognizing its given form or its form after completing the square.

Find the gradient of the function at the given point.

Find the limit.

Find symmetric equations of the tangent line to the curve of intersection of the surfaces , at the point . ​

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

Find a unit normal vector to the surface at the point .

Find the limit for the function . ​

Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places. ​

Find the absolute extrema of on the region bounded by the square with vertices and . ​

Find the critical points of the function , and from the form of the function, determine whether a relative maximum or a relative minimum occurs at each point.

Find a unit normal vector to the surface at the point .

Find for function .

Use Lagrange multipliers to find the maximum value of where and subject to the constraint . ​

Find using the appropriate Chain Rule for where , and . ​

Find the partial derivative for the function . ​

Use Lagrange multipliers to find the minimum distance from the parabola to the point . Round your answer to two decimal places. ​

Find the angle of inclination of the tangent plane to the surface at the point . Round your answer to two decimal places.

​Find the partial derivative for the function . ​

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function at the critical point , if . ​

Find symmetric equations of the tangent line to the curve of intersection of the surfaces , at the point .

Find the limit for the function .

Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places.

Find the absolute extrema of on the region bounded by the square with vertices and .

Use Lagrange multipliers to find the maximum value of where and subject to the constraint .

Find using the appropriate Chain Rule for where , and .

Find the partial derivative for the function .

Use Lagrange multipliers to find the minimum distance from the parabola to the point . Round your answer to two decimal places.

Find the partial derivative for the function .

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function at the critical point , if .