Question 1

Let   . Describe the level surface passing through   .

Accepted Answer

A)  Ellipsoid 
B)  Hyperboloid of one sheet 
C)  Elliptical cone 
D)  Hyperboloid of two sheets 
E)  Hyperbolic paraboloid 
A)  Ellipsoid 
B)  Hyperboloid of one sheet 
C)  Elliptical cone 
D)  Hyperboloid of two sheets 
E)  Hyperbolic paraboloid

Question 2

Let   . Find the slope of the surface   in the y-direction at the point   .

Accepted Answer

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

Question 3

Sketch the graph of   in xyz space and label three points on the surface.

Accepted Answer

x = 6 , y

Question 4

Let   . Find   if   .

Accepted Answer

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

Question 5

Show that   is continuous at (0, 0).

Accepted Answer

Let r² = x² + y², then

Question 6

Use Lagrange multipliers to find all the locations of the extreme values of   subject to   .

Accepted Answer

A)  (0, 0) 
B)    ,
  
C)    ,
 
  ,
  
D)    ,
 
  ,
  
E)  There are none 
A)  (0, 0) 
B)    ,
  
C)    ,
 
  ,
  
D)    ,
 
  ,
  
E)  There are none

Question 7

The power consumed in an electrical resistor is given by   watts. Suppose E =   volts and R =   ohms, approximate the change in power if E is increased by   volts and R is decreased by   ohms.

Accepted Answer

The power

Question 8

Let   , find   . Round your answer to three decimal places.

Accepted Answer

The answer of Let   , find  ...

Question 9

Let   . There is a critical point at

Accepted Answer

A)  (0, 0) 
B)    
C)    
D)  none exist 
E)  (1, 1) 
A)  (0, 0) 
B)    
C)    
D)  none exist 
E)  (1, 1)

Question 10

Let   ; Find   .

Accepted Answer

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

Question 11

Use the chain rule to find   if w = 4 + sin xy + y ln xz + z and x = et , y = t2, z = 1.

Accepted Answer

t²e ^t cos t²e

Question 12

Let   . Find   .

Accepted Answer

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

Question 13

A rectangular box is to contain   cubic inches. Find the dimensions of the box for which the surface area is a minimum.

Accepted Answer

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

Question 14

Evaluate   .

Accepted Answer

The limit

Question 15

Let z = 5 + 4 sin(x2y4). Find   .

Accepted Answer

A)    
B)  2xy3 cos(x2y4) 
C)  y3 cos(x2y4) 
D)  16x2y3 cos(x2y4) 
E)  x2 cos(x2y4) 
A)    
B)  2xy3 cos(x2y4) 
C)  y3 cos(x2y4) 
D)  16x2y3 cos(x2y4) 
E)  x2 cos(x2y4)

Question 16

Sketch the graph of   in xyz space.

Accepted Answer

X = 4 ; Y

Question 17

Find the equations of the tangent plane and normal line to   at   .Express the equation of the normal line parametrically.

Accepted Answer

The equation of the

Question 18

Use Lagrange multipliers to find the maximum and minimum values of   subject to   .

Accepted Answer

A)  No maximum or minimum values. 
B)  The maximum value is   and the minimum value is
  
C)  The maximum value is   and the minimum value is
  
D)  The maximum value is   , and the minimum value is
  
E)  The maximum value is   , and the minimum value is
  
A)  No maximum or minimum values. 
B)  The maximum value is   and the minimum value is
  
C)  The maximum value is   and the minimum value is
  
D)  The maximum value is   , and the minimum value is
  
E)  The maximum value is   , and the minimum value is

Question 19

Find parametric equations for the normal line to   at   .

Accepted Answer

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

Question 20

Find d $ \omega $ if

Accepted Answer

The answer of Find d $ \omega $ if ...

Let . Describe the level surface passing through .

Let . Find the slope of the surface in the y-direction at the point .

Sketch the graph of in xyz space and label three points on the surface.

Let . Find if .

Show that is continuous at (0, 0).

Use Lagrange multipliers to find all the locations of the extreme values of subject to .

The power consumed in an electrical resistor is given by watts. Suppose E = volts and R = ohms, approximate the change in power if E is increased by volts and R is decreased by ohms.

Let , find . Round your answer to three decimal places.

Let . There is a critical point at

Let ; Find .

Use the chain rule to find if w = 4 + sin xy + y ln xz + z and x = e^t , y = t², z = 1.

Let . Find .

A rectangular box is to contain cubic inches. Find the dimensions of the box for which the surface area is a minimum.

Evaluate .

Let z = 5 + 4 sin(x²y⁴). Find .

Sketch the graph of in xyz space.

Find the equations of the tangent plane and normal line to at .Express the equation of the normal line parametrically.

Use Lagrange multipliers to find the maximum and minimum values of subject to .

Find parametric equations for the normal line to at .

Find d $\omega$ if $Find d \omega if$

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

Let . Describe the level surface passing through .

Let . Find the slope of the surface in the y-direction at the point .

Sketch the graph of in xyz space and label three points on the surface.

Let . Find if .

Show that is continuous at (0, 0).

Use Lagrange multipliers to find all the locations of the extreme values of subject to .

The power consumed in an electrical resistor is given by watts. Suppose E = volts and R = ohms, approximate the change in power if E is increased by volts and R is decreased by ohms.

Let , find . Round your answer to three decimal places.

Let . There is a critical point at

Let ; Find .

Use the chain rule to find if w = 4 + sin xy + y ln xz + z and x = et , y = t2, z = 1.

Let . Find .

A rectangular box is to contain cubic inches. Find the dimensions of the box for which the surface area is a minimum.

Evaluate .

Let z = 5 + 4 sin(x2y4). Find .

Sketch the graph of in xyz space.

Find the equations of the tangent plane and normal line to at .Express the equation of the normal line parametrically.

Use Lagrange multipliers to find the maximum and minimum values of subject to .

Find parametric equations for the normal line to at .

Find d ω \omega ω if

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

Use the chain rule to find if w = 4 + sin xy + y ln xz + z and x = e^t , y = t², z = 1.

Let z = 5 + 4 sin(x²y⁴). Find .

Find d $\omega$ if $Find d \omega if$