Question 1

Find the area of the common interior of the polar equations   and   by sketching the graph of the equations using the graphing utility. ​

Accepted Answer

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

Question 2

Find the vertex of the parabola given by   . ​

Accepted Answer

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

Question 3

Find the component form of vector v given its magnitude is   and the angle it makes with the positive x-axis is   . ​

Accepted Answer

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

Question 4

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 34 yards directly downfield at a height of 3 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) 0.8 second 
B) 4.6 seconds 
C) 7.8 seconds 
D) 1.3 seconds 
E) 2.6 seconds 
A) 0.8 second 
B) 4.6 seconds 
C) 7.8 seconds 
D) 1.3 seconds 
E) 2.6 seconds

Question 5

Given the vector-valued function below,evaluate   . ​   ​

Accepted Answer

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

Question 6

Write the corresponding rectangular equation for the curve represented by the parametric equations   by eliminating the parameter. ​

Accepted Answer

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

Question 7

Find   given the functions below. ​   ​

Accepted Answer

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

Question 8

Find an equation of the parabola with vertex   and directrix   . ​

Accepted Answer

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

Question 9

Find the foci of the ellipse given by   . ​

Accepted Answer

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

Question 10

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 11

​What is the total distance traveled by the particle in the time interval   ? Round your answer to three decimal places.

Accepted Answer

The answer of ​What is the total distance traveled by...

Question 12

The path of a projectile is modeled by the parametric equations   and   where x and y are measured in feet.Use a graphing utility to approximate the range of the projectile.Round your answer to two decimal places. ​

Accepted Answer

A) 327.75 ft 
B) 546.25 ft 
C) 137.33 ft 
D) 409.68 ft 
E) 204.84 ft 
A) 327.75 ft 
B) 546.25 ft 
C) 137.33 ft 
D) 409.68 ft 
E) 204.84 ft

Question 13

The parametric equations for the path of a projectile launched at a height h feet above the ground,at an angle θ with the horizontal and having an initial velocity of v0 feet per second is given by   and   .The center field fence in a ballpark is 10 feet high and 400 feet from home plate.The ball is hit   feet above the ground.It leaves the bat at an angle of θ degrees with the horizontal at a speed of 100 miles per hour as shown in the figure.Write a set of parametric equations for the path of the ball. ​   ​

Accepted Answer

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

Find the area of the common interior of the polar equations and by sketching the graph of the equations using the graphing utility.

Find the vertex of the parabola given by .

Find the component form of vector v given its magnitude is and the angle it makes with the positive x-axis is .

Given the vector-valued function below,evaluate .

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.

Find given the functions below.

Find an equation of the parabola with vertex and directrix .

Find the foci of the ellipse given by .

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

What is the total distance traveled by the particle in the time interval ? Round your answer to three decimal places.

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet.Use a graphing utility to approximate the range of the projectile.Round your answer to two decimal places.

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 the area of the common interior of the polar equations and by sketching the graph of the equations using the graphing utility. ​

Find the vertex of the parabola given by . ​

Find the component form of vector v given its magnitude is and the angle it makes with the positive x-axis is . ​

Given the vector-valued function below,evaluate . ​ ​

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter. ​

Find given the functions below. ​ ​

Find an equation of the parabola with vertex and directrix . ​

Find the foci of the ellipse given by . ​

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

​What is the total distance traveled by the particle in the time interval ? Round your answer to three decimal places.

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet.Use a graphing utility to approximate the range of the projectile.Round your answer to two decimal places. ​

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 the area of the common interior of the polar equations and by sketching the graph of the equations using the graphing utility.

Find the vertex of the parabola given by .

Find the component form of vector v given its magnitude is and the angle it makes with the positive x-axis is .

Given the vector-valued function below,evaluate .

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.

Find given the functions below.

Find an equation of the parabola with vertex and directrix .

Find the foci of the ellipse given by .

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

What is the total distance traveled by the particle in the time interval ? Round your answer to three decimal places.

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet.Use a graphing utility to approximate the range of the projectile.Round your answer to two decimal places.