Question 1

Find an equation of the tangent plane to the given surface at the specified point.

Accepted Answer

The answer of Find an equation of the tangent plane...

Question 2

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s. At what rate is the volume of the cone changing when the radius is   in. and the height is   in.?

Accepted Answer

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

Question 3

The length l, width w and height h of a box change with time. At a certain instant the dimensions are   and   , and l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s. At that instant find the rates at which the surface area is changing.

Accepted Answer

The answer of The length l, width w and height...

Question 4

Find the shortest distance from the point   to the plane   .

Accepted Answer

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

Question 5

Find three positive numbers whose sum is   and whose product is a maximum.

Accepted Answer

The answer of Find three positive numbers whose sum is...

Question 6

Find three positive numbers whose sum is   and whose product is a maximum.

Accepted Answer

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

Question 7

Use implicit differentiation to find

Accepted Answer

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

Question 8

Use the Chain Rule to find   where   .

Accepted Answer

The answer of Use the Chain Rule to find ...

Question 9

A contour map for a function f is shown. Use it to estimate the value of   .

Accepted Answer

A) 35 
B) 28 
C) 48 
D)    
E) 78 
A) 35 
B) 28 
C) 48 
D)    
E) 78

Question 10

Suppose that over a certain region of space the electrical potential V is given by   .Find the rate of change of the potential at   in the direction of the vector   .

Accepted Answer

A) 20 
B) 44 
C)    
D) -2.91 
E)    
A) 20 
B) 44 
C)    
D) -2.91 
E)

Question 11

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of   ,   ,   what can you say about f ?

Accepted Answer

A) f has a saddle point at (1,1) 
B) f has a local minimum at (1,1) 
C) f has a local maximum at (1,1) 
A) f has a saddle point at (1,1) 
B) f has a local minimum at (1,1) 
C) f has a local maximum at (1,1)

Question 12

Find the first partial derivatives of the function.

Accepted Answer

The answer of Find the first partial derivatives of the...

Question 13

Find the critical points of the function.

Accepted Answer

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

Find an equation of the tangent plane to the given surface at the specified point.

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s. At what rate is the volume of the cone changing when the radius is in. and the height is in.?

The length l, width w and height h of a box change with time. At a certain instant the dimensions are and , and l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s. At that instant find the rates at which the surface area is changing.

Find the shortest distance from the point to the plane .

Find three positive numbers whose sum is and whose product is a maximum.

Find three positive numbers whose sum is and whose product is a maximum.

Use implicit differentiation to find

Use the Chain Rule to find where .

A contour map for a function f is shown. Use it to estimate the value of .

Suppose that over a certain region of space the electrical potential V is given by .Find the rate of change of the potential at in the direction of the vector .

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of , , what can you say about f ?

Find the first partial derivatives of the function.

Find the critical points of the function.

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 an equation of the tangent plane to the given surface at the specified point.

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s. At what rate is the volume of the cone changing when the radius is in. and the height is in.?

The length l, width w and height h of a box change with time. At a certain instant the dimensions are and , and l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 1 m/s. At that instant find the rates at which the surface area is changing.

Find the shortest distance from the point to the plane .

Find three positive numbers whose sum is and whose product is a maximum.

Find three positive numbers whose sum is and whose product is a maximum.

Use implicit differentiation to find

Use the Chain Rule to find where .

A contour map for a function f is shown. Use it to estimate the value of .

Suppose that over a certain region of space the electrical potential V is given by .Find the rate of change of the potential at in the direction of the vector .

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of , , what can you say about f ?

Find the first partial derivatives of the function.

Find the critical points of the function.

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