Question 1

Let   . There is a critical point at

Accepted Answer

A)  (10, 4) 
B)  (5, 2) 
C)    
D)  (0, 0) 
E)  (1, 1) 
A)  (10, 4) 
B)  (5, 2) 
C)    
D)  (0, 0) 
E)  (1, 1)

Question 2

At t = 0, the position of a particle on a rectangular membrane is given by   . Find the rate at which P changes if the particle moves from   in a direction of a vector making an angle 30° with the positive x-axis.

Accepted Answer

The answer of At t = 0, the position of...

Question 3

Use the total differential to approximate the change in   as (x, y) varies from   to   .

Accepted Answer

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

Question 4

Find the slope of the surface   in the x-direction at the point (1, 5, 25e).

Accepted Answer

The answer of Find the slope of the surface ...

Question 5

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

Accepted Answer

The answer of Determine whether the limit exists. If so,...

Question 6

The sides of a rectangle are measured to be   and   cm with a maximum error of   cm in each measurement. Use differentials to estimate the maximum possible error in the calculated value of the area.

Accepted Answer

A)    is the maximum error in the area. 
B)    is the maximum error in the area. 
C)    is the maximum error in the area. 
D)    is the maximum error in the area. 
E)    is the maximum error in the area. 
A)    is the maximum error in the area. 
B)    is the maximum error in the area. 
C)    is the maximum error in the area. 
D)    is the maximum error in the area. 
E)    is the maximum error in the area.

Question 7

Use the chain rule to find   . z = 5x2y + 12; x = t3, y = t2

Accepted Answer

Question 8

Let   . Compute the differential dz.

Accepted Answer

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

Question 9

Let   . Find   .

Accepted Answer

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

Question 10

Use Lagrange multipliers to find the volume of the largest rectangular box that can be inscribed within the ellipsoid   .

Accepted Answer

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

Question 11

Use the total differential to approximate the change in   as (x, y) varies from   to   .

Accepted Answer

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

Question 12

Compute the local linear approximation to   at   .

Accepted Answer

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

Question 13

Find the total differential of f(x, y, z) = 6e-5xyz .

Accepted Answer

df = -30yz

Question 14

Let   . Find   .

Accepted Answer

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

Question 15

Find the point on   that is closest to the origin.

Accepted Answer

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

Question 16

Let   ;   . Using the chain rule, find   .

Accepted Answer

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

Question 17

Find the equations of the tangent plane and normal line to z = xesin y at (2,  $\pi$, 5).Express the equation of the normal line parametrically.

Accepted Answer

The equation of the tangent pl

Question 18

Find d $ \omega $ if   .

Accepted Answer

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

Question 19

Let   ; x = u + v , y = u - v. Find   .

Accepted Answer

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

Question 20

Evaluate   .

Accepted Answer

A)  648 
B)  7004 
C)  -3567 
D)  Does not exist 
E)  36 
A)  648 
B)  7004 
C)  -3567 
D)  Does not exist 
E)  36

Let . There is a critical point at

At t = 0, the position of a particle on a rectangular membrane is given by . Find the rate at which P changes if the particle moves from in a direction of a vector making an angle 30° with the positive x-axis.

Use the total differential to approximate the change in as (x, y) varies from to .

Find the slope of the surface in the x-direction at the point (1, 5, 25e).

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

The sides of a rectangle are measured to be and cm with a maximum error of cm in each measurement. Use differentials to estimate the maximum possible error in the calculated value of the area.

Use the chain rule to find . z = 5x²y + 12; x = t³, y = t²

Let . Compute the differential dz.

Let . Find .

Use Lagrange multipliers to find the volume of the largest rectangular box that can be inscribed within the ellipsoid .

Use the total differential to approximate the change in as (x, y) varies from to .

Compute the local linear approximation to at .

Find the total differential of f(x, y, z) = 6e^-⁵^xyz .

Let . Find .

Find the point on that is closest to the origin.

Let ; . Using the chain rule, find .

Find the equations of the tangent plane and normal line to z = xe^sin^y at (2, $\pi$ , 5).Express the equation of the normal line parametrically.

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

Let ; x = u + v , y = u - v. Find .

Evaluate .

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 . There is a critical point at

At t = 0, the position of a particle on a rectangular membrane is given by . Find the rate at which P changes if the particle moves from in a direction of a vector making an angle 30° with the positive x-axis.

Use the total differential to approximate the change in as (x, y) varies from to .

Find the slope of the surface in the x-direction at the point (1, 5, 25e).

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

The sides of a rectangle are measured to be and cm with a maximum error of cm in each measurement. Use differentials to estimate the maximum possible error in the calculated value of the area.

Use the chain rule to find . z = 5x2y + 12; x = t3, y = t2

Let . Compute the differential dz.

Let . Find .

Use Lagrange multipliers to find the volume of the largest rectangular box that can be inscribed within the ellipsoid .

Use the total differential to approximate the change in as (x, y) varies from to .

Compute the local linear approximation to at .

Find the total differential of f(x, y, z) = 6e-5xyz .

Let . Find .

Find the point on that is closest to the origin.

Let ; . Using the chain rule, find .

Find the equations of the tangent plane and normal line to z = xesin y at (2, π\piπ , 5).Express the equation of the normal line parametrically.

Find d ω \omega ω if .

Let ; x = u + v , y = u - v. Find .

Evaluate .

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 . z = 5x²y + 12; x = t³, y = t²

Find the total differential of f(x, y, z) = 6e^-⁵^xyz .

Find the equations of the tangent plane and normal line to z = xe^sin^y at (2, $\pi$ , 5).Express the equation of the normal line parametrically.

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