Question 1

Find   at the point   for the equation   . ​

Accepted Answer

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

Question 2

Find   by implicit differentiation. ​   ​

Accepted Answer

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

Question 3

Find the derivative of the function   . ​

Accepted Answer

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

Question 4

Find an equation of the tangent line to the graph of   at the point (0,1). ​

Accepted Answer

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

Question 5

Find an equation to the tangent line to the graph of the function   at the point   .The coefficients below are given to two decimal places. ​

Accepted Answer

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

Question 6

A spherical balloon is inflated with gas at the rate of 900 cubic centimeters per minute.How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters? ​

Accepted Answer

A)    cm/min 
B)    cm/min 
C)    cm/min 
D)    cm/min 
E)    cm/min 
A)    cm/min 
B)    cm/min 
C)    cm/min 
D)    cm/min 
E)    cm/min

Question 7

Find the second derivative of the function. ​   ​

Accepted Answer

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

Question 8

A buoy oscillates in simple harmonic motion   as waves move past it.The buoy moves a total of 11.5 feet (vertically)between its low point and its high point.It returns to its high point every 10 seconds.Determine the velocity of the buoy as a function of t. ​

Accepted Answer

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

Question 9

Find an equation of the line that is tangent to the graph of the function   and parallel to the line   . ​​

Accepted Answer

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

Question 10

Approximate the positive zero(s)of the function   to three decimal places.Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. ​

Accepted Answer

A) -1.304 
B) 1.202 
C) 1.179 
D) -1.202 
E) 1.253 
A) -1.304 
B) 1.202 
C) 1.179 
D) -1.202 
E) 1.253

Question 11

Find the derivative of the algebraic function   . ​

Accepted Answer

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

Question 12

Find the derivative of the function   . ​

Accepted Answer

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

Question 13

Use the alternative form of the derivative to find the derivative of the function   at   . ​

Accepted Answer

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

Question 14

Find the derivative of the trigonometric function   . ​

Accepted Answer

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

Question 15

Use implicit differentiation to find   . ​   ​

Accepted Answer

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

Question 16

Find an equation of the tangent line to the graph of   at the point (1,0). ​

Accepted Answer

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

Question 17

Find the derivative of the function   .Simplify your answer. ​

Accepted Answer

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

Question 18

Find   at the point   for the equation   . ​

Accepted Answer

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

Question 19

If the annual rate of inflation averages 4% over the next 10 years,the approximate cost C of goods or services during any year in that decade is   where t is the time in years and P is the present cost.The price of an oil change for your car is presently $24.75.Find the rate of change of C with respect to t when   .Round your answer to three decimal places. ​

Accepted Answer

A) 38.101 dollars per year 
B) 1.010 dollars per year 
C) 1.437 dollars per year 
D) 10.644 dollars per year 
E) 84.358 dollars per year 
A) 38.101 dollars per year 
B) 1.010 dollars per year 
C) 1.437 dollars per year 
D) 10.644 dollars per year 
E) 84.358 dollars per year

Question 20

Find the second derivative of the function   . ​

Accepted Answer

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

Find at the point for the equation .

Find by implicit differentiation.

Find the derivative of the function .

Find an equation of the tangent line to the graph of at the point (0,1).

Find an equation to the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places.

A spherical balloon is inflated with gas at the rate of 900 cubic centimeters per minute.How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters?

Find the second derivative of the function.

A buoy oscillates in simple harmonic motion as waves move past it.The buoy moves a total of 11.5 feet (vertically)between its low point and its high point.It returns to its high point every 10 seconds.Determine the velocity of the buoy as a function of t.

Find an equation of the line that is tangent to the graph of the function and parallel to the line .

Approximate the positive zero(s)of the function to three decimal places.Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.

Find the derivative of the algebraic function .

Find the derivative of the function .

Use the alternative form of the derivative to find the derivative of the function at .

Find the derivative of the trigonometric function .

Use implicit differentiation to find .

Find an equation of the tangent line to the graph of at the point (1,0).

Find the derivative of the function .Simplify your answer.

Find at the point for the equation .

Find the second derivative of the function .

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

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

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 3: Differentiation

Find at the point for the equation . ​

Find by implicit differentiation. ​ ​

Find the derivative of the function . ​

Find an equation of the tangent line to the graph of at the point (0,1). ​

Find an equation to the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places. ​

A spherical balloon is inflated with gas at the rate of 900 cubic centimeters per minute.How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters? ​

Find the second derivative of the function. ​ ​

A buoy oscillates in simple harmonic motion as waves move past it.The buoy moves a total of 11.5 feet (vertically)between its low point and its high point.It returns to its high point every 10 seconds.Determine the velocity of the buoy as a function of t. ​

Find an equation of the line that is tangent to the graph of the function and parallel to the line . ​​

Approximate the positive zero(s)of the function to three decimal places.Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. ​

Find the derivative of the algebraic function . ​

Find the derivative of the function . ​

Use the alternative form of the derivative to find the derivative of the function at . ​

Find the derivative of the trigonometric function . ​

Use implicit differentiation to find . ​ ​

Find an equation of the tangent line to the graph of at the point (1,0). ​

Find the derivative of the function .Simplify your answer. ​

Find at the point for the equation . ​

Find the second derivative of the function . ​

Preparation for Calculus

Limits and Their Properties

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

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

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find at the point for the equation .

Find by implicit differentiation.

Find the derivative of the function .

Find an equation of the tangent line to the graph of at the point (0,1).

Find an equation to the tangent line to the graph of the function at the point .The coefficients below are given to two decimal places.

A spherical balloon is inflated with gas at the rate of 900 cubic centimeters per minute.How fast is the radius of the balloon increasing at the instant the radius is 70 centimeters?

Find the second derivative of the function.

A buoy oscillates in simple harmonic motion as waves move past it.The buoy moves a total of 11.5 feet (vertically)between its low point and its high point.It returns to its high point every 10 seconds.Determine the velocity of the buoy as a function of t.

Find an equation of the line that is tangent to the graph of the function and parallel to the line .

Approximate the positive zero(s)of the function to three decimal places.Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.

Find the derivative of the algebraic function .

Find the derivative of the function .

Use the alternative form of the derivative to find the derivative of the function at .

Find the derivative of the trigonometric function .

Use implicit differentiation to find .

Find an equation of the tangent line to the graph of at the point (1,0).

Find the derivative of the function .Simplify your answer.

Find at the point for the equation .

Find the second derivative of the function .