Question 1

Match the following vector-valued function with its graph. ​  ​

Accepted Answer

B

Question 2

Evaluate  , where  and S is the closed surface of the solid bounded by the graphs,  and  , and the coordinate planes. ​

Accepted Answer

B

Question 3

Let  and let S be the graph of  . Verify Stokes's Theorem by evaluating  as a line integral and as a double integral.
​

Accepted Answer

D

Question 4

Use Stokes's Theorem to evaluate  where  and S is the first-octant portion of  over  . Use a computer algebra system to verify your result. ​

Accepted Answer

The answer of Use Stokes's Theorem to evaluate  where...

Question 5

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function  and sketch the graph. ​

Accepted Answer

The answer of Find the rectangular equation for the surface...

Question 6

Use Stokes's Theorem to evaluate  . Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.

Accepted Answer

The answer of Use Stokes's Theorem to evaluate  ....

Question 7

Match the following vector-valued function with its graph. ​

Accepted Answer

The answer of Match the following vector-valued function with its...

Question 8

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path  given in polar coordinates is  " to find the area of the region bounded by the graphs of the polar equation  . ​

Accepted Answer

The answer of Use a computer algebra system and the...

Question 9

Let  and let S be the surface bounded by  and  . Verify the Divergence Theorem by evaluating  as a surface integral and as a triple integral. Round your answer to two decimal places.
​

Accepted Answer

The answer of Let  and let S be the...

Question 10

Use Green's Theorem to evaluate the integral  for the path  defined as  . ​

Accepted Answer

The answer of Use Green's Theorem to evaluate the integral...

Question 11

Set up and evaluate a line integral to find the area of the region R bounded by the graph of  .

Accepted Answer

The answer of Set up and evaluate a line integral...

Question 12

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function  . ​

Accepted Answer

The answer of Find the rectangular equation for the surface...

Question 13

Calculate the line integral along  for  and C is any path starting at the point  and ending at  . ​

Accepted Answer

The answer of Calculate the line integral along  for...

Question 14

The surface of the dome on a new museum is given by  , where  and  and  is in meters. Find the surface area of the dome. ​

Accepted Answer

The answer of The surface of the dome on a...

Question 15

Find the curl of the vector field  . ​

Accepted Answer

The answer of Find the curl of the vector field...

Question 16

Sketch several representative vectors in the vector field given by  . ​

Accepted Answer

The answer of Sketch several representative vectors in the vector...

Question 17

Find a vector-valued function for the hyperboloid  . ​

Accepted Answer

The answer of Find a vector-valued function for the hyperboloid...

Question 18

Find the work done by a person weighing  pounds walking exactly one revolution up a circular helical staircase of radius  feet if the person rises  feet.

Accepted Answer

The answer of Find the work done by a person...

Question 19

Sketch the vector field  . ​

Accepted Answer

The answer of Sketch the vector field  . ​
...

Question 20

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path  given in polar coordinates is  " to find the area of the region bounded by the graphs of the polar equation  . Round your answer to two decimal places. ​

Accepted Answer

The answer of Use a computer algebra system and the...

Quiz 15: Vector Anal

Match the following vector-valued function with its graph. ​ ​

Evaluate , where and S is the closed surface of the solid bounded by the graphs, and , and the coordinate planes. ​

Let and let S be the graph of . Verify Stokes's Theorem by evaluating as a line integral and as a double integral. ​

Use Stokes's Theorem to evaluate where and S is the first-octant portion of over . Use a computer algebra system to verify your result. ​

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function and sketch the graph. ​

Use Stokes's Theorem to evaluate . Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.

Match the following vector-valued function with its graph. ​

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation . ​

Let and let S be the surface bounded by and . Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral. Round your answer to two decimal places. ​

Use Green's Theorem to evaluate the integral for the path defined as . ​

Set up and evaluate a line integral to find the area of the region R bounded by the graph of .

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function . ​

Calculate the line integral along for and C is any path starting at the point and ending at . ​

The surface of the dome on a new museum is given by , where and and is in meters. Find the surface area of the dome. ​

Find the curl of the vector field . ​

Sketch several representative vectors in the vector field given by . ​

Find a vector-valued function for the hyperboloid . ​

Find the work done by a person weighing pounds walking exactly one revolution up a circular helical staircase of radius feet if the person rises feet.

Sketch the vector field . ​

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation . Round your answer to two decimal places. ​

Match the following vector-valued function with its graph.

Evaluate , where and S is the closed surface of the solid bounded by the graphs, and , and the coordinate planes.

Let and let S be the graph of . Verify Stokes's Theorem by evaluating as a line integral and as a double integral.

Use Stokes's Theorem to evaluate where and S is the first-octant portion of over . Use a computer algebra system to verify your result.

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function and sketch the graph.

Match the following vector-valued function with its graph.

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation .

Let and let S be the surface bounded by and . Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral. Round your answer to two decimal places.

Use Green's Theorem to evaluate the integral for the path defined as .

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function .

Calculate the line integral along for and C is any path starting at the point and ending at .

The surface of the dome on a new museum is given by , where and and is in meters. Find the surface area of the dome.

Find the curl of the vector field .

Sketch several representative vectors in the vector field given by .

Find a vector-valued function for the hyperboloid .

Sketch the vector field .

Use a computer algebra system and the result "The area of a plane region bounded by the simple closed path given in polar coordinates is " to find the area of the region bounded by the graphs of the polar equation . Round your answer to two decimal places.