Question 1

Sketch, by hand, the curve traced out by the given vector-valued function.

Accepted Answer

The answer of Sketch, by hand, the curve traced out...

Question 2

Compute the arc length. 
A) 
B) 
C) 
D)

Accepted Answer

A

Question 3

Find the limit if it exists. 
A) 
B) 
C) 
D) does not exist

Accepted Answer

C

Question 4

Sketch, by hand, the curve traced out by the given vector-valued function.

Accepted Answer

The answer of Sketch, by hand, the curve traced out...

Question 5

Find the limit if it exists. 
A) 
B) 
C) 
D) does not exist

Accepted Answer

There is not enough information provided to determine the limit.

Question 6

Match the vector-valued function with its graph. 
A) 
B) 
C) 
D)

Accepted Answer

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

Question 7

Use graphing technology to sketch the curve traced out by the given vector-valued function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use graphing technology to sketch the curve...

Question 8

Use a CAS to estimate the arc length of the curve. 
A) 16.1
B) 13.6
C) 14.1
D) 18.2

Accepted Answer

The answer of Use a CAS to estimate the arc...

Question 9

Use a CAS to estimate the arc length of the curve. 
A) 21.4
B) 84.8
C) 33.8
D) 7.6

Accepted Answer

The answer of Use a CAS to estimate the arc...

Question 10

Use graphing technology to sketch the curve traced out by the given vector-valued function.  Use the viewpoint  and  (see figure below). 
A) 
B) 
C) 
D)

Accepted Answer

Using the given viewpoint, we can see that the curve is traced out in the xy-plane, and it appears to be a circle centered at (0,0) with radius 1. Plugging in different values of t into the function, we can confirm that this is indeed a circle. Choice A matches this description, while the other choices do not.

Question 11

Determine all values of t at which the given vector-valued function is continuous. 
A) 
B) 
C) 
D) all real numbers

Accepted Answer

The answer of Determine all values of t at which...

Question 12

Find parametric equations for the indicated curve.
The intersection of  and z = 2

Accepted Answer

The answer of Find parametric equations for the indicated curve.
The...

Question 13

Sketch, by hand, the curve traced out by the given vector-valued function.

Accepted Answer

The answer of Sketch, by hand, the curve traced out...

Question 14

Phillip claims that the trajectory  for  is identical to the trajectory  for  , where t represents time. Sharon suggests that Phillip's claim is not necessarily true. Who is correct and why?

Accepted Answer

The answer of Phillip claims that the trajectory  for...

Question 15

Use graphing technology to sketch the curve traced out by the given vector-valued function.  Use the viewpoint  and  (see figure below). 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use graphing technology to sketch the curve...

Question 16

Show that the curve  lies on the elliptical paraboloid  . Show all your work.

Accepted Answer

The answer of Show that the curve  lies on...

Question 17

Match the vector-valued function with its graph. 
A) 
B) 
C) 
D)

Accepted Answer

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

Question 18

Determine all values of t at which the given vector-valued function is continuous. 
A) 
B) 
C) 
D) all real numbers

Accepted Answer

The answer of Determine all values of t at which...

Question 19

Find parametric equations for the indicated curve.
The intersection of  and x + y = 2

Accepted Answer

The answer of Find parametric equations for the indicated curve.
The...

Question 20

Match the vector-valued function with its graph. 
A) 
B) 
C) 
D)

Accepted Answer

The graph of A is a parabolic path in the xy-plane, which indicates a projectile motion. The x and y components of the vector function are both quadratic functions, indicating a parabolic path. The other graphs do not have this property. B and C are helixes in three dimensions, and D is a spiral in the xy-plane.

Quiz 12: Vector-Valued Functions

Sketch, by hand, the curve traced out by the given vector-valued function.

Compute the arc length.

Find the limit if it exists.

Sketch, by hand, the curve traced out by the given vector-valued function.

Find the limit if it exists.

Match the vector-valued function with its graph.

Use graphing technology to sketch the curve traced out by the given vector-valued function.

Use a CAS to estimate the arc length of the curve.

Use a CAS to estimate the arc length of the curve.

Use graphing technology to sketch the curve traced out by the given vector-valued function. Use the viewpoint and (see figure below) .

Determine all values of t at which the given vector-valued function is continuous.

Find parametric equations for the indicated curve. The intersection of and z = 2

Sketch, by hand, the curve traced out by the given vector-valued function.

Phillip claims that the trajectory for is identical to the trajectory for , where t represents time. Sharon suggests that Phillip's claim is not necessarily true. Who is correct and why?

Use graphing technology to sketch the curve traced out by the given vector-valued function. Use the viewpoint and (see figure below) .

Show that the curve lies on the elliptical paraboloid . Show all your work.

Match the vector-valued function with its graph.

Determine all values of t at which the given vector-valued function is continuous.

Find parametric equations for the indicated curve. The intersection of and x + y = 2

Match the vector-valued function with its graph.