Question 1

Use the properties of the derivative to find  given the following vector-valued functions.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 3.2 miles to make a  turn and climb to an altitude of 3.4 miles. The model for the path of the plane during this maneuver is  where t is the time in hours and r is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.

Accepted Answer

A)  201 mi/h 
B)  64 mi/h 
C)  173 mi/h 
D)  137 mi/h 
E)  255 mi/h

Question 3

Find the indefinite integral below.  Do not include an arbitrary constant vector.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Find  given the functions below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Find the unit tangent vector to the curve given below at the specified point.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Find the curvature  of the curve given below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Find the domain of the vector-valued function given below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find the radius of curvature of the plane curve  at  . Round your answer to three decimal places.

Accepted Answer

A)  1021.045 
B)  2340.571 
C)  1374.626 
D)  1565.001 
E)  1571.001

Question 9

Evaluate the definite integral below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Find  given the following vector function. ​  ​

Accepted Answer

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

Question 11

A baseball player at second base throws a ball 95 feet to the player at first base. The ball is thrown 8 feet above the ground with an initial velocity of 46 miles per hour and at an angle of  above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.

Accepted Answer

A)  2.908 feet 
B)  2.008 feet 
C)  0.808 feet 
D)  1.408 feet 
E)  0.908 feet

Question 12

Find  given the following vector function. ​  ​

Accepted Answer

A)  1 
B)  -18  
C)  18  
D)  0 
E)  3

Question 13

Find  at time  for the plane curve  . Round your answer to three decimal places.

Accepted Answer

A)  4.575 
B)  3.841 
C)  2.716 
D)  1.718 
E)  4.685

Question 14

Use the properties of the derivative to find  given the following vector-valued functions.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter

Accepted Answer

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

Question 16

A baseball is hit 5 feet above the ground at 160 feet per second and at an angle of  with respect to the ground. Find the vector-valued function for the path of the baseball.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of  with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place. ​

Accepted Answer

A)  194.2 feet 
B)  212.3 feet 
C)  210.1 feet 
D)  171.4 feet 
E)  236.5 feet

Question 18

Find  at time  for the space curve  . Round your answer to three decimal places.

Accepted Answer

A)  0.041 
B)  0.093 
C)  0.406 
D)  0.000 
E)  0.914

Question 19

The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 78 yards directly downfield at a height of 4 feet. The pass is released at an angle of  with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.

Accepted Answer

A)  2.2 seconds 
B)  12.8 seconds 
C)  22.2 seconds 
D)  3.7 seconds 
E)  7.4 seconds

Question 20

The position vector  describes the path of an object moving in space. Find the velocity  of the object.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 12: Vector-Valued Functions

Use the properties of the derivative to find given the following vector-valued functions.

Find the indefinite integral below. Do not include an arbitrary constant vector.

Find given the functions below.

Find the unit tangent vector to the curve given below at the specified point.

Find the curvature of the curve given below.

Find the domain of the vector-valued function given below.

Find the radius of curvature of the plane curve at . Round your answer to three decimal places.

Evaluate the definite integral below.

Find given the following vector function. ​ ​

Find given the following vector function. ​ ​

Find at time for the plane curve . Round your answer to three decimal places.

Use the properties of the derivative to find given the following vector-valued functions.

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter

A baseball is hit 5 feet above the ground at 160 feet per second and at an angle of with respect to the ground. Find the vector-valued function for the path of the baseball.

A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place. ​

Find at time for the space curve . Round your answer to three decimal places.

The position vector describes the path of an object moving in space. Find the velocity of the object.

Find given the following vector function.

Find given the following vector function.

A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place.