Question 1

Find an equation for the tangent plane to   at   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Let   . Find   .

Accepted Answer

The answer of Let   . Find  ...

Question 3

A particle is located at the point (2, 7) on a metal surface whose temperature at a point (x, y) is T(x, y) = 16 - 2x2 - 3y2. Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

Accepted Answer

A)    
B)    
C)    
D)    
E)  1 
A)    
B)    
C)    
D)    
E)  1

Question 4

Locate all relative maxima, relative minima, and saddle points for
f(x, y) = x2 - xy + y 2 + 2x + 2y - 3.

Accepted Answer

(-2, -2);

Question 5

Let   . Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Find all points on the surface z = xe-y + 8 at which the tangent plane is horizontal.

Accepted Answer

There are no points

Question 7

Let   ; Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find parametric equations for the normal line to   at   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Use the Lagrange multiplier method to find the point on the surface z = xy + 10 that is closest to the origin.

Accepted Answer

(3, 3, 1)

Question 10

Compute the total differential for the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Sketch the graph of   in xyz space.

Accepted Answer

The answer of Sketch the graph of   in...

Question 12

Let   . Find   if   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Describe the family of level curves for z = 4x2 + y2(z $\ge$ 0) and sketch a few of these curves.

Accepted Answer

The family of level

Question 14

Let f(x, y) = 4 + ln(xy). Find f y (2, 3).

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Let   ;   Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the rate of change of   at   in the direction of   .

Accepted Answer

The answer of Find the rate of change of ...

Question 17

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 18

Determine whether the limit exists. If so, find its value.

Accepted Answer

The limit

Question 19

Find the total differential of f(x, y, z) = 3 + x4y5z2.

Accepted Answer

df = 4x³y⁵z²d

Question 20

Let   ; Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find an equation for the tangent plane to at .

Let . Find .

A particle is located at the point (2, 7) on a metal surface whose temperature at a point (x, y) is T(x, y) = 16 - 2x² - 3y². Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

Locate all relative maxima, relative minima, and saddle points for f(x, y) = x² - xy + y ² + 2x + 2y - 3.

Let . Find .

Find all points on the surface z = xe^-y + 8 at which the tangent plane is horizontal.

Let ; Find .

Find parametric equations for the normal line to at .

Use the Lagrange multiplier method to find the point on the surface z = xy + 10 that is closest to the origin.

Compute the total differential for the function .

Sketch the graph of in xyz space.

Let . Find if .

Describe the family of level curves for z = 4x² + y²(z $\ge$ 0) and sketch a few of these curves.

Let f(x, y) = 4 + ln(xy). Find f _y (2, 3).

Let ; Find .

Find the rate of change of at in the direction of .

Evaluate .

Determine whether the limit exists. If so, find its value.

Find the total differential of f(x, y, z) = 3 + x⁴y⁵z².

Let ; Find .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 13: Partial Derivatives

Find an equation for the tangent plane to at .

Let . Find .

A particle is located at the point (2, 7) on a metal surface whose temperature at a point (x, y) is T(x, y) = 16 - 2x2 - 3y2. Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

Locate all relative maxima, relative minima, and saddle points for f(x, y) = x2 - xy + y 2 + 2x + 2y - 3.

Let . Find .

Find all points on the surface z = xe-y + 8 at which the tangent plane is horizontal.

Let ; Find .

Find parametric equations for the normal line to at .

Use the Lagrange multiplier method to find the point on the surface z = xy + 10 that is closest to the origin.

Compute the total differential for the function .

Sketch the graph of in xyz space.

Let . Find if .

Describe the family of level curves for z = 4x2 + y2(z ≥\ge≥ 0) and sketch a few of these curves.

Let f(x, y) = 4 + ln(xy). Find f y (2, 3).

Let ; Find .

Find the rate of change of at in the direction of .

Evaluate .

Determine whether the limit exists. If so, find its value.

Find the total differential of f(x, y, z) = 3 + x4y5z2.

Let ; Find .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Multiple Integrals

Topics in Vector Calculus

Filters

A particle is located at the point (2, 7) on a metal surface whose temperature at a point (x, y) is T(x, y) = 16 - 2x² - 3y². Find the equation for the trajectory of a particle moving continuously in the direction of maximum temperature increase. y =

Locate all relative maxima, relative minima, and saddle points for f(x, y) = x² - xy + y ² + 2x + 2y - 3.

Find all points on the surface z = xe^-y + 8 at which the tangent plane is horizontal.

Describe the family of level curves for z = 4x² + y²(z $\ge$ 0) and sketch a few of these curves.

Let f(x, y) = 4 + ln(xy). Find f _y (2, 3).

Find the total differential of f(x, y, z) = 3 + x⁴y⁵z².