Question 1

Find   given the following vector function. ​   ​

Accepted Answer

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

Question 2

Match the equation with its graph. ​   ​

Accepted Answer

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

Question 3

Find the vertices of the ellipse given by   . ​

Accepted Answer

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

Question 4

Find the area of the region lying between the loops of   . ​

Accepted Answer

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

Question 5

Use the result,"the set of parametric equations for the ellipse is   " to find a set of parametric equations for the ellipse with vertices   and   and with foci at   and   . ​

Accepted Answer

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

Question 6

Find the area of the surface formed by revolving about the   axis the following curve over the given interval. ​   ​

Accepted Answer

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

Question 7

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 8

A particle moving in the xy-plane has acceleration vector   for all   .The particle is at rest at time   .
-Give the velocity vector of at time   .

Accepted Answer

The answer of A particle moving in the xy-plane has...

Question 9

​A particle moving in the xy-plane has a position vector   for   .The acceleration vector of the particle is ​

Accepted Answer

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

Question 10

Determine the t intervals on which the curve   ,   is concave downward or concave upward. ​

Accepted Answer

A) concave downward:   ;concave upward:
  
B) concave downward:   ;concave upward:
  
C) concave downward:   ;concave upward:
  
D) concave downward:   ;concave upward:
  
E) concave downward:   ;concave upward:
  
A) concave downward:   ;concave upward:
  
B) concave downward:   ;concave upward:
  
C) concave downward:   ;concave upward:
  
D) concave downward:   ;concave upward:
  
E) concave downward:   ;concave upward:

Question 11

Three forces with magnitudes 80 pounds,110 pounds and 25 pounds act on an object at angles 30°,-70°,and 120° respectively,with the positive x-axis.Find the direction and magnitude of the resultant force.(The choices below are given to two decimal places. ) ​

Accepted Answer

A) 136.12 pounds at angle of - 66.16° with the positive x-axis 
B) 103.21 pounds at angle of 23.84° with the positive x-axis 
C) 103.21 pounds at angle of - 66.16° with the positive x-axis 
D) 136.12 pounds at angle of - 23.84° with the positive x-axis 
E) 103.21 pounds at angle of - 23.84° with the positive x-axis 
A) 136.12 pounds at angle of - 66.16° with the positive x-axis 
B) 103.21 pounds at angle of 23.84° with the positive x-axis 
C) 103.21 pounds at angle of - 66.16° with the positive x-axis 
D) 136.12 pounds at angle of - 23.84° with the positive x-axis 
E) 103.21 pounds at angle of - 23.84° with the positive x-axis

Question 12

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 13

Find the center of the ellipse given by   . ​

Accepted Answer

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

Question 14

Find the center,foci,vertices,and eccentricity of the ellipse. ​     ​

Accepted Answer

A) center:   vertices:
  foci:
  eccentricity:
  
B) center:   vertices:
  foci:
  eccentricity:
  
C) center:   vertices:
  foci:
  eccentricity:
  
D) center:   vertices:
  foci:
  eccentricity:
  
E) center:   vertices:
  foci:
  eccentricity:
  
A) center:   vertices:
  foci:
  eccentricity:
  
B) center:   vertices:
  foci:
  eccentricity:
  
C) center:   vertices:
  foci:
  eccentricity:
  
D) center:   vertices:
  foci:
  eccentricity:
  
E) center:   vertices:
  foci:
  eccentricity:

Question 15

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​   ​

Accepted Answer

A) circle 
B) hyperbola 
C) ellipse 
D) parabola 
A) circle 
B) hyperbola 
C) ellipse 
D) parabola

Question 16

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 17

Find the vector v whose initial and terminal points are given below. ​
(5,5), (7,2)
​

Accepted Answer

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

Question 18

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 19

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

Accepted Answer

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

Question 20

Find all points (if any)of horizontal and vertical tangency to the curve   ,   .

Accepted Answer

A) horizontal tangents:   ,vertical tangents:
  
B) horizontal tangents:   ,vertical tangents:
  
C) horizontal tangent:   ,vertical tangent:
  
D) horizontal tangents:   ,vertical tangents:
  
E) horizontal tangent:   ,vertical tangent:
  
A) horizontal tangents:   ,vertical tangents:
  
B) horizontal tangents:   ,vertical tangents:
  
C) horizontal tangent:   ,vertical tangent:
  
D) horizontal tangents:   ,vertical tangents:
  
E) horizontal tangent:   ,vertical tangent:

Find given the following vector function.

Match the equation with its graph.

Find the vertices of the ellipse given by .

Find the area of the region lying between the loops of .

Use the result,"the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and .

Find the area of the surface formed by revolving about the axis the following curve over the given interval.

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

A particle moving in the xy-plane has acceleration vector for all .The particle is at rest at time . -Give the velocity vector of at time .

A particle moving in the xy-plane has a position vector for .The acceleration vector of the particle is

Determine the t intervals on which the curve , is concave downward or concave upward.

Three forces with magnitudes 80 pounds,110 pounds and 25 pounds act on an object at angles 30°,-70°,and 120° respectively,with the positive x-axis.Find the direction and magnitude of the resultant force.(The choices below are given to two decimal places. )

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

Find the center of the ellipse given by .

Find the center,foci,vertices,and eccentricity of the ellipse.

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

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

Find the vector v whose initial and terminal points are given below. (5,5), (7,2)

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 .

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

Find all points (if any)of horizontal and vertical tangency to the curve , .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 10: Parametric Equations, Polar Coordinates, and Vectors

Find given the following vector function. ​ ​

Match the equation with its graph. ​ ​

Find the vertices of the ellipse given by . ​

Find the area of the region lying between the loops of . ​

Use the result,"the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and . ​

Find the area of the surface formed by revolving about the axis the following curve over the given interval. ​ ​

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

A particle moving in the xy-plane has acceleration vector for all .The particle is at rest at time . -Give the velocity vector of at time .

​A particle moving in the xy-plane has a position vector for .The acceleration vector of the particle is ​

Determine the t intervals on which the curve , is concave downward or concave upward. ​

Three forces with magnitudes 80 pounds,110 pounds and 25 pounds act on an object at angles 30°,-70°,and 120° respectively,with the positive x-axis.Find the direction and magnitude of the resultant force.(The choices below are given to two decimal places. ) ​

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

Find the center of the ellipse given by . ​

Find the center,foci,vertices,and eccentricity of the ellipse. ​ ​

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​ ​

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

Find the vector v whose initial and terminal points are given below. ​ (5,5), (7,2) ​

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 . ​

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

Find all points (if any)of horizontal and vertical tangency to the curve , .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find given the following vector function.

Match the equation with its graph.

Find the vertices of the ellipse given by .

Find the area of the region lying between the loops of .

Use the result,"the set of parametric equations for the ellipse is " to find a set of parametric equations for the ellipse with vertices and and with foci at and .

Find the area of the surface formed by revolving about the axis the following curve over the given interval.

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

A particle moving in the xy-plane has a position vector for .The acceleration vector of the particle is

Determine the t intervals on which the curve , is concave downward or concave upward.

Three forces with magnitudes 80 pounds,110 pounds and 25 pounds act on an object at angles 30°,-70°,and 120° respectively,with the positive x-axis.Find the direction and magnitude of the resultant force.(The choices below are given to two decimal places. )

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

Find the center of the ellipse given by .

Find the center,foci,vertices,and eccentricity of the ellipse.

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

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

Find the vector v whose initial and terminal points are given below. (5,5), (7,2)

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 .

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