Question 1

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

Accepted Answer

A)  5.315 
B)  3.010 
C)  7.491 
D)  3.745 
E)  2.657 
A)  5.315 
B)  3.010 
C)  7.491 
D)  3.745 
E)  2.657

Question 2

Find   given the following vector function. ​   ​

Accepted Answer

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

Question 3

Use the given acceleration function and initial conditions to find the position at time t = 1.

Accepted Answer

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

Question 4

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 maximum height. Round your answer to the nearest integer.

Accepted Answer

A)  247 feet 
B)  235 feet 
C)  205 feet 
D)  218 feet 
E)  220 feet 
A)  247 feet 
B)  235 feet 
C)  205 feet 
D)  218 feet 
E)  220 feet

Question 5

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

Accepted Answer

A)  28.451 
B)  28.636 
C)  28.400 
D)  28.111 
E)  20.897 
A)  28.451 
B)  28.636 
C)  28.400 
D)  28.111 
E)  20.897

Question 6

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

Accepted Answer

A)  -30.406 
B)  -29.533 
C)  -81.262 
D)  -35.346 
E)  -33.994 
A)  -30.406 
B)  -29.533 
C)  -81.262 
D)  -35.346 
E)  -33.994

Question 7

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

Accepted Answer

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

Question 8

Find the unit tangent vector   for the line tangent to the space curve   at point   .

Accepted Answer

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

Question 9

The position vector   describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point   .

Accepted Answer

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

Question 10

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)    
A)    
B)    
C)    
D)    
E)

Question 11

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

Accepted Answer

A)  0.816 
B)  0.389 
C)  0.777 
D)  1.864 
E)  0.889 
A)  0.816 
B)  0.389 
C)  0.777 
D)  1.864 
E)  0.889

Question 12

A particle moves in the yz-plane along the curve represented by the vector-valued function   . Find the minimum value of   .

Accepted Answer

A)  3 
B)  2 
C)  5 
D)  6 
E)  8 
A)  3 
B)  2 
C)  5 
D)  6 
E)  8

Question 13

A baseball, hit 3 feet above the ground, leaves the bat at an angle of   and is caught by an outfielder 3 feet above the ground and 300 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.

Accepted Answer

A)  24.49 ft/sec 
B)  97.98 ft/sec 
C)  146.97 ft/sec 
D)  122.47 ft/sec 
E)  48.99 ft/sec 
A)  24.49 ft/sec 
B)  97.98 ft/sec 
C)  146.97 ft/sec 
D)  122.47 ft/sec 
E)  48.99 ft/sec

Question 14

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

Accepted Answer

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

Question 15

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 30 yards directly downfield at a height of 5 feet. The pass is released at an angle of   with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.

Accepted Answer

A)  32.979 feet per second 
B)  57.483 feet per second 
C)  18.863 feet per second 
D)  114.967 feet per second 
E)  189.144 feet per second 
A)  32.979 feet per second 
B)  57.483 feet per second 
C)  18.863 feet per second 
D)  114.967 feet per second 
E)  189.144 feet per second

Question 16

Find the vectors   and   for the following vector function. ​   ​

Accepted Answer

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

Question 17

A 5800-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.

Accepted Answer

A)  2,716.9 lb 
B)  3,396.4 lb 
C)  3,046.0 lb 
D)  2,707.6 lb 
E)  3,565.1 lb 
A)  2,716.9 lb 
B)  3,396.4 lb 
C)  3,046.0 lb 
D)  2,707.6 lb 
E)  3,565.1 lb

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

A)  1.069 
B)  0.963 
C)  0.468 
D)  0.936 
E)  0.848 
A)  1.069 
B)  0.963 
C)  0.468 
D)  0.936 
E)  0.848

Question 20

Evaluate the limit given below. ​   ​

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)  The limit does not exist.
​ 
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)  The limit does not exist.
​

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

Find given the following vector function.

Use the given acceleration function and initial conditions to find the position at time t = 1.

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 maximum height. Round your answer to the nearest integer.

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

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

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

Find the unit tangent vector for the line tangent to the space curve at point .

The position vector describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .

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

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

A particle moves in the yz-plane along the curve represented by the vector-valued function . Find the minimum value of .

A baseball, hit 3 feet above the ground, leaves the bat at an angle of and is caught by an outfielder 3 feet above the ground and 300 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.

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

Find the vectors and for the following vector function.

A 5800-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.

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

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

Evaluate the limit given below.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 12: Vector-Valued Functions

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

Find given the following vector function. ​ ​

Use the given acceleration function and initial conditions to find the position at time t = 1.

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 maximum height. Round your answer to the nearest integer.

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

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

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

Find the unit tangent vector for the line tangent to the space curve at point .

The position vector describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .

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

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

A particle moves in the yz-plane along the curve represented by the vector-valued function . Find the minimum value of .

A baseball, hit 3 feet above the ground, leaves the bat at an angle of and is caught by an outfielder 3 feet above the ground and 300 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.

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

Find the vectors and for the following vector function. ​ ​

A 5800-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.

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

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

Evaluate the limit given below. ​ ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find given the following vector function.

Find the vectors and for the following vector function.

Evaluate the limit given below.