Question 1

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

The answer of The radius of a right circular cone...

Question 2

Find the differential of the function

Accepted Answer

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

Question 3

Use the Chain Rule to find

Accepted Answer

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

Question 4

Find equations for the tangent plane and the normal line to the surface with equation  at the point

Accepted Answer

The answer of Find equations for the tangent plane and...

Question 5

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

The answer of Use differentials to estimate the amount of...

Question 6

Find the directional derivative of the function  at the point  in the direction of the unit vector that makes the angle  with the positive x-axis.

Accepted Answer

The answer of Find the directional derivative of the function...

Question 7

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

The answer of Suppose that over a certain region of...

Question 8

Find  for the function

Accepted Answer

The answer of Find  for the function 
...

Question 9

Use the Chain Rule to find  .

Accepted Answer

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

Question 10

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)

Accepted Answer

The answer of Use differentials to estimate the amount of...

Question 11

Find  for the function  .

Accepted Answer

The answer of Find  for the function  .
...

Question 12

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

Accepted Answer

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

Question 13

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 14

Use the Chain Rule to find  where  .

Accepted Answer

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

Question 15

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

Accepted Answer

The answer of Find the equation of the normal line...

Question 16

Find the differential of the function

Accepted Answer

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

Question 17

If  use the gradient vector  to find the tangent line to the level curve  at the point  .

Accepted Answer

The answer of If  use the gradient vector ...

Question 18

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

Accepted Answer

The answer of Let  and suppose that  changes...

Question 19

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

Accepted Answer

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

Question 20

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...

Quiz 11: Partial Derivatives

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.?

Find the differential of the function

Use the Chain Rule to find

Find equations for the tangent plane and the normal line to the surface with equation at the point

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.

Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis.

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 .

Find for the function

Use the Chain Rule to find .

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)

Find for the function .

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

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.

Use the Chain Rule to find where .

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

Find the differential of the function

If use the gradient vector to find the tangent line to the level curve at the point .

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

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

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