Question 1

Find and sketch the domain of the function

Accepted Answer

The answer of Find and sketch the domain of the...

Question 2

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Accepted Answer

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

Question 3

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height   cm if the tin is 0.04 cm thick.

Accepted Answer

14.07

Question 4

How many nth-order partial derivatives does a function of two variables have?

Accepted Answer

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

Question 5

Find the limit

Accepted Answer

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

Question 6

Find the absolute extrema of the function   on the closed triangular region with vertices   ,   and   .

Accepted Answer

A) Absolute minimum 5, Absolute maximum 17 
B) Absolute minimum 0, Absolute maximum 5 
C) Absolute minimum -5, Absolute maximum 5 
D) Absolute minimum -5, Absolute maximum 17 
A) Absolute minimum 5, Absolute maximum 17 
B) Absolute minimum 0, Absolute maximum 5 
C) Absolute minimum -5, Absolute maximum 5 
D) Absolute minimum -5, Absolute maximum 17

Question 7

Find the absolute minimum value of the function   on the set D. D is the region bounded by the parabola   and the line

Accepted Answer

A) 0 
B)    
C)    
D)    
E) 30 
A) 0 
B)    
C)    
D)    
E) 30

Question 8

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Accepted Answer

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

Question 9

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 10

Use implicit differentiation to find

Accepted Answer

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

Question 11

Find the limit

Accepted Answer

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

Question 12

Find the equation of the normal line to the given surface at the specified point.

Accepted Answer

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

Question 13

Use spherical coordinates to find the limit.

Accepted Answer

The answer of Use spherical coordinates to find the limit....

Question 14

If R is the total resistance of three resistors, connected in parallel, with resistances   , then   .If the resistances are measured in ohms as   , with a possible error of 0.8% in each case, estimate the maximum error in the calculated value of R.

Accepted Answer

A) 0.291   
B) 0.476   
C) 0.347   
D) 0.957   
E) 0.098   
A) 0.291   
B) 0.476   
C) 0.347   
D) 0.957   
E) 0.098

Question 15

Find the local maximum, and minimum value and saddle points of the function.

Accepted Answer

Min at @#IMG-DLM& , @#IMG-DLM& , Max poi

Question 16

Find the points on the surface   that are closest to the origin.

Accepted Answer

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

Question 17

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Accepted Answer

maximum =

Question 18

Use the definition of partial derivatives as limits to find   if   .

Accepted Answer

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

Question 19

Find the limit

Accepted Answer

A) 34 
B) 260 
C) 80 
D) 16 
A) 34 
B) 260 
C) 80 
D) 16

Question 20

Let   and suppose that   changes from   to   (a) Compute   (b) Compute

Accepted Answer

The answer of Let   and suppose that ...

Find and sketch the domain of the function

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height cm if the tin is 0.04 cm thick.

How many nth-order partial derivatives does a function of two variables have?

Find the limit

Find the absolute extrema of the function on the closed triangular region with vertices , and .

Find the absolute minimum value of the function on the set D. D is the region bounded by the parabola and the line

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Find the differential of the function.

Use implicit differentiation to find

Find the limit

Find the equation of the normal line to the given surface at the specified point.

Use spherical coordinates to find the limit.

If R is the total resistance of three resistors, connected in parallel, with resistances , then .If the resistances are measured in ohms as , with a possible error of 0.8% in each case, estimate the maximum error in the calculated value of R.

Find the local maximum, and minimum value and saddle points of the function.

Find the points on the surface that are closest to the origin.

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Use the definition of partial derivatives as limits to find if .

Find the limit

Let and suppose that changes from to (a) Compute (b) Compute

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Multiple Integrals

Vector Calculus

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Exam 11: Partial Derivatives

Find and sketch the domain of the function

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height cm if the tin is 0.04 cm thick.

How many nth-order partial derivatives does a function of two variables have?

Find the limit

Find the absolute extrema of the function on the closed triangular region with vertices , and .

Find the absolute minimum value of the function on the set D. D is the region bounded by the parabola and the line

Use Lagrange multipliers to find the minimum value of the function subject to the given constraints.

Find the differential of the function.

Use implicit differentiation to find

Find the limit

Find the equation of the normal line to the given surface at the specified point.

Use spherical coordinates to find the limit.

If R is the total resistance of three resistors, connected in parallel, with resistances , then .If the resistances are measured in ohms as , with a possible error of 0.8% in each case, estimate the maximum error in the calculated value of R.

Find the local maximum, and minimum value and saddle points of the function.

Find the points on the surface that are closest to the origin.

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Use the definition of partial derivatives as limits to find if .

Find the limit

Let and suppose that changes from to (a) Compute (b) Compute

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Multiple Integrals

Vector Calculus

Filters