Question 1

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)    E

Question 2

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

Accepted Answer

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

Question 3

Find the curvature K of the curve   at the point   . Round your answer to three decimal places.

Accepted Answer

A)  0.728 
B)  0.970 
C)  0.158 
D)  0.057 
E)  0.126 
A)  0.728 
B)  0.970 
C)  0.158 
D)  0.057 
E)  0.126 D

Question 4

Find the curvature K of the curve   at the point   . Round your answer to three decimal places.

Accepted Answer

A)  1.400 
B)  1.599 
C)  0.192 
D)  0.435 
E)  0.053 
A)  1.400 
B)  1.599 
C)  0.192 
D)  0.435 
E)  0.053

Question 5

Find   given the following vector function. ​   ​

Accepted Answer

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

Question 6

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

Accepted Answer

A)  0.986 
B)  0.658 
C)  0.114 
D)  0.036 
E)  0.027 
A)  0.986 
B)  0.658 
C)  0.114 
D)  0.036 
E)  0.027

Question 7

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 8

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

Accepted Answer

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

Question 9

Sketch the curve represented by the vector-valued function   and give the orientation of the curve.

Accepted Answer

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

Question 10

Find the open interval on which the curve given by the vector-valued function   is smooth.

Accepted Answer

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

Question 11

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 12

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.

Question 13

Find   given the following. ​   ​

Accepted Answer

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

Question 14

Represent the following curve by a vector-valued function.

Accepted Answer

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

Question 15

Given the vector-valued function below, evaluate   .

Accepted Answer

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

Question 16

Find the length of the space curve given below.

Accepted Answer

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

Question 17

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

Accepted Answer

A)      
B)    122 
C)      
D)      
E)    18 
A)      
B)    122 
C)      
D)      
E)    18

Question 18

Find the point on the curve given below at which the curvature K is zero.

Accepted Answer

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

Question 19

A baseball is hit 3 feet above the ground at 95 feet per second and at an angle of   with respect to the ground. Find the range. Round your answer to one decimal place.

Accepted Answer

A)  285 feet 
B)  352.2 feet 
C)  370.7 feet 
D)  501.9 feet 
E)  300 feet 
A)  285 feet 
B)  352.2 feet 
C)  370.7 feet 
D)  501.9 feet 
E)  300 feet

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)    
A)    
B)    
C)    
D)    
E)

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

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

Find the curvature K of the curve at the point . Round your answer to three decimal places.

Find the curvature K of the curve at the point . Round your answer to three decimal places.

Find given the following vector function.

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

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

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

Sketch the curve represented by the vector-valued function and give the orientation of the curve.

Find the open interval on which the curve given by the vector-valued function is smooth.

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

Evaluate the limit given below.

Find given the following.

Represent the following curve by a vector-valued function.

Given the vector-valued function below, evaluate .

Find the length of the space curve given below.

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

Find the point on the curve given below at which the curvature K is zero.

A baseball is hit 3 feet above the ground at 95 feet per second and at an angle of with respect to the ground. Find the range. Round your answer to one decimal place.

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

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

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

Find the curvature K of the curve at the point . Round your answer to three decimal places.

Find the curvature K of the curve at the point . Round your answer to three decimal places.

Find given the following vector function. ​ ​

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

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

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

Sketch the curve represented by the vector-valued function and give the orientation of the curve.

Find the open interval on which the curve given by the vector-valued function is smooth.

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

Evaluate the limit given below.

Find given the following. ​ ​

Represent the following curve by a vector-valued function.

Given the vector-valued function below, evaluate .

Find the length of the space curve given below.

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

Find the point on the curve given below at which the curvature K is zero.

A baseball is hit 3 feet above the ground at 95 feet per second and at an angle of with respect to the ground. Find the range. Round your answer to one decimal place.

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

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 given the following.

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