Question 1

Find the derivative of the following function using the limiting process. ​   ​

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Question 2

Find   at the point   for the equation   . ​

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Question 3

Find the derivative of the trigonometric function   . ​

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Question 4

Find the slope-intercept equation of the line tangent to the graph of   when   . ​

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Question 5

Find the derivative of the function   . ​

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Question 6

A buoy oscillates in simple harmonic motion   as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0. ​

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Question 7

Find the derivative of the function   by the limit process. ​

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Question 8

Find   in terms of x and y. ​   ​

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Question 9

Use the Quotient Rule to differentiate the function   . ​

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Question 10

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

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Question 11

Use Newton's Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places. Continue the process until two successive approximations differ by less than 0.001. [Hint: Let

Accepted Answer

A)  2.651 
B)  2.703 
C)  2.660 
D)  2.764 
E)  2.600 
A)  2.651 
B)  2.703 
C)  2.660 
D)  2.764 
E)  2.600

Question 12

Find the derivative of the function   . ​

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Question 13

Use the quotient rule to differentiate the following function   and evaluate   . ​

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Question 14

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

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Question 15

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when   inches. ​

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Question 16

Assume that x and y are both differentiable functions of t. Find   when   and   for the equation   . ​

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Question 17

Find the derivative of the function   . ​

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Question 18

Use the rules of differentiation to find the derivative of the function   . ​

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Question 19

Find   by implicit differentiation given that   . Use the original equation to simplify your answer. ​

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Question 20

Find   if   . ​

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Find the derivative of the following function using the limiting process.

Find at the point for the equation .

Find the derivative of the trigonometric function .

Find the slope-intercept equation of the line tangent to the graph of when .

Find the derivative of the function .

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0.

Find the derivative of the function by the limit process.

Find in terms of x and y.

Use the Quotient Rule to differentiate the function .

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

Use Newton's Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places. Continue the process until two successive approximations differ by less than 0.001. [Hint: Let

Find the derivative of the function .

Use the quotient rule to differentiate the following function and evaluate .

Find the derivative of the function . Simplify your answer.

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when inches.

Assume that x and y are both differentiable functions of t. Find when and for the equation .

Find the derivative of the function .

Use the rules of differentiation to find the derivative of the function .

Find by implicit differentiation given that . Use the original equation to simplify your answer.

Find if .

Preparation for Calculus

Limits and Their Properties

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

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 3: Differentiation

Find the derivative of the following function using the limiting process. ​ ​

Find at the point for the equation . ​

Find the derivative of the trigonometric function . ​

Find the slope-intercept equation of the line tangent to the graph of when . ​

Find the derivative of the function . ​

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0. ​

Find the derivative of the function by the limit process. ​

Find in terms of x and y. ​ ​

Use the Quotient Rule to differentiate the function . ​

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

Use Newton's Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places. Continue the process until two successive approximations differ by less than 0.001. [Hint: Let

Find the derivative of the function . ​

Use the quotient rule to differentiate the following function and evaluate . ​

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

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when inches. ​

Assume that x and y are both differentiable functions of t. Find when and for the equation . ​

Find the derivative of the function . ​

Use the rules of differentiation to find the derivative of the function . ​

Find by implicit differentiation given that . Use the original equation to simplify your answer. ​

Find if . ​

Preparation for Calculus

Limits and Their Properties

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

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find the derivative of the following function using the limiting process.

Find at the point for the equation .

Find the derivative of the trigonometric function .

Find the slope-intercept equation of the line tangent to the graph of when .

Find the derivative of the function .

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 10.5 feet (vertically) between its low point and its high point. It returns to its high point every 16 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0.

Find the derivative of the function by the limit process.

Find in terms of x and y.

Use the Quotient Rule to differentiate the function .

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

Find the derivative of the function .

Use the quotient rule to differentiate the following function and evaluate .

Find the derivative of the function . Simplify your answer.

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when inches.

Assume that x and y are both differentiable functions of t. Find when and for the equation .

Find the derivative of the function .

Use the rules of differentiation to find the derivative of the function .

Find by implicit differentiation given that . Use the original equation to simplify your answer.

Find if .