Question 1

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 2

Let   . Find   and   .

Accepted Answer

The answer of Let   . Find  ...

Question 3

Let   . Find   .

Accepted Answer

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

Question 4

Let   . Find an equation of the level surface passing through   .

Accepted Answer

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

Question 5

Use the chain rule to find   and   if w = 4 + ln(x2 + y2 + z2), x = e r cos s, y = e r sin s, z = e s .

Accepted Answer

Question 6

Find the slope of the surface z = 12x2y3 in the y-direction at the point (1, 2, 96).

Accepted Answer

Question 7

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 8

Find an equation for the tangent plane to   at   .

Accepted Answer

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

Question 9

Find the point(s) on   that are closest to   .

Accepted Answer

A)    
B)    
C)    , and
  
D)  (0, 0, 0) and (1, 1, 1) 
E)    
A)    
B)    
C)    , and
  
D)  (0, 0, 0) and (1, 1, 1) 
E)

Question 10

Let   . Compute the differential dz.

Accepted Answer

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

Question 11

Find an equation for the tangent plane to   at   .

Accepted Answer

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

Question 12

Find   and   if z = x3 + xy - y cos xy + 2.

Accepted Answer

Question 13

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 14

Let   . Describe the level surface passing through   .

Accepted Answer

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

Question 15

Find f x (x, y) and f y (x, y) if f(x, y) = 5 + x y .

Accepted Answer

Question 16

Evaluate   .

Accepted Answer

A)    
B)    
C)    
D)  Does not exist 
E)  6 
A)    
B)    
C)    
D)  Does not exist 
E)  6

Question 17

For the gas law   = RT, where R is a constant, estimate the change in RT as P goes from 1atm to 1.001atm and V goes from 2m3 to 2.003m3. Answer in atm·m3.

Accepted Answer

A)  0.00250 
B)  0.00300 
C)  0.00200 
D)  0.00150 
E)  0.0100 
A)  0.00250 
B)  0.00300 
C)  0.00200 
D)  0.00150 
E)  0.0100

Question 18

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

Accepted Answer

A)  The maximum value is 0, and there is no minimum value. 
B)  The maximum value is   and the minimum value is
  
C)  The minimum value is 0, and there is no maximum value. 
D)  The minimum value is   , and there is no maximum value. 
E)  The maximum value is   and the minimum value is 0. 
A)  The maximum value is 0, and there is no minimum value. 
B)  The maximum value is   and the minimum value is
  
C)  The minimum value is 0, and there is no maximum value. 
D)  The minimum value is   , and there is no maximum value. 
E)  The maximum value is   and the minimum value is 0.

Question 19

Let   . Find   if   .

Accepted Answer

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

Question 20

Use implicit differentiation to find   and   if x2z2 - 2xyz + y2z3 = 12.

Accepted Answer

Evaluate .

Let . Find and .

Let . Find .

Let . Find an equation of the level surface passing through .

Use the chain rule to find and if w = 4 + ln(x² + y² + z²), x = e ^r cos s, y = e ^r sin s, z = e ^s .

Find the slope of the surface z = 12x²y³ in the y-direction at the point (1, 2, 96).

Evaluate .

Find an equation for the tangent plane to at .

Find the point(s) on that are closest to .

Let . Compute the differential dz.

Find an equation for the tangent plane to at .

Find and if z = x³ + xy - y cos xy + 2.

Evaluate .

Let . Describe the level surface passing through .

Find f _x (x, y) and f _y (x, y) if f(x, y) = 5 + x ^y .

Evaluate .

For the gas law = RT, where R is a constant, estimate the change in RT as P goes from 1atm to 1.001atm and V goes from 2m³ to 2.003m³. Answer in atm·m³.

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

Let . Find if .

Use implicit differentiation to find and if x²z² - 2xyz + y²z³ = 12.

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

Evaluate .

Let . Find and .

Let . Find .

Let . Find an equation of the level surface passing through .

Use the chain rule to find and if w = 4 + ln(x2 + y2 + z2), x = e r cos s, y = e r sin s, z = e s .

Find the slope of the surface z = 12x2y3 in the y-direction at the point (1, 2, 96).

Evaluate .

Find an equation for the tangent plane to at .

Find the point(s) on that are closest to .

Let . Compute the differential dz.

Find an equation for the tangent plane to at .

Find and if z = x3 + xy - y cos xy + 2.

Evaluate .

Let . Describe the level surface passing through .

Find f x (x, y) and f y (x, y) if f(x, y) = 5 + x y .

Evaluate .

For the gas law = RT, where R is a constant, estimate the change in RT as P goes from 1atm to 1.001atm and V goes from 2m3 to 2.003m3. Answer in atm·m3.

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

Let . Find if .

Use implicit differentiation to find and if x2z2 - 2xyz + y2z3 = 12.

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 and if w = 4 + ln(x² + y² + z²), x = e ^r cos s, y = e ^r sin s, z = e ^s .

Find the slope of the surface z = 12x²y³ in the y-direction at the point (1, 2, 96).

Find and if z = x³ + xy - y cos xy + 2.

Find f _x (x, y) and f _y (x, y) if f(x, y) = 5 + x ^y .

For the gas law = RT, where R is a constant, estimate the change in RT as P goes from 1atm to 1.001atm and V goes from 2m³ to 2.003m³. Answer in atm·m³.

Use implicit differentiation to find and if x²z² - 2xyz + y²z³ = 12.