Question 1

Complete two iterations of Newton's Method for the function   using the initial guess 2.2. Round your answers to four decimal places. ​

Accepted Answer

A)  2.2365, 2.2359 
B)  2.2365, 2.2363 
C)  2.2365, 2.2362 
D)  2.2362, 2.2360 
E)  2.2364, 2.2361 
A)  2.2365, 2.2359 
B)  2.2365, 2.2363 
C)  2.2365, 2.2362 
D)  2.2362, 2.2360 
E)  2.2364, 2.2361

Question 2

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

Accepted Answer

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

Question 3

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 4

Find the slope   of the line tangent to the graph of the function   at the point   . ​

Accepted Answer

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

Question 5

Use the general rule to approximate   and   to three decimal places. ​   ,   ​

Accepted Answer

A)  1.73749, 1.61401 
B)  1.65922, 1.99377 
C)  1.28355, 1.44311 
D)  1.56530, 1.89883 
A)  1.73749, 1.61401 
B)  1.65922, 1.99377 
C)  1.28355, 1.44311 
D)  1.56530, 1.89883

Question 6

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 7

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 8

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when   . ​

Accepted Answer

A)  -130 ft/sec 
B)  -34 ft/sec 
C)  -21 ft/sec 
D)  -195 ft/sec 
E)  -65 ft/sec 
A)  -130 ft/sec 
B)  -34 ft/sec 
C)  -21 ft/sec 
D)  -195 ft/sec 
E)  -65 ft/sec

Question 9

Use implicit differentiation to find   at the point   . ​   ​

Accepted Answer

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

Question 10

Find   if   . ​

Accepted Answer

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

Question 11

Approximate the fixed point of the function   between   and   to two decimal places. [A fixed point   of a function f is a value of x such that   .] ​

Accepted Answer

A)  0.65 
B)  0.74 
C)  0 
D)  1.00 
E)  0.91 
A)  0.65 
B)  0.74 
C)  0 
D)  1.00 
E)  0.91

Question 12

A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 19 feet from the wall. Round your answer to three decimal places. ​   ​

Accepted Answer

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

Question 13

Suppose that an automobile's velocity starting from rest is   where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place. ​

Accepted Answer

A)  1.1 ft/sec2 
B)  1.8 ft/sec2 
C)  1.0 ft/sec2 
D)  0.2 ft/sec2 
E)  12.4 ft/sec2 
A)  1.1 ft/sec2 
B)  1.8 ft/sec2 
C)  1.0 ft/sec2 
D)  0.2 ft/sec2 
E)  12.4 ft/sec2

Question 14

Use the Product Rule to differentiate. ​   ​

Accepted Answer

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

Question 15

Find the derivative of the algebraic function   . ​

Accepted Answer

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

Question 16

Find an equation to the tangent line for the graph of f at the given point. ​   ,   ​

Accepted Answer

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

Question 17

The length of a rectangle is   and its height is   , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. ​

Accepted Answer

A)    square inches/second 
B)    square inches/second 
C)    square inches/second 
D)    square inches/second 
E)    square inches/second 
A)    square inches/second 
B)    square inches/second 
C)    square inches/second 
D)    square inches/second 
E)    square inches/second

Question 18

Find the slope of the graph of the function at the given value. ​   when   ​

Accepted Answer

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

Question 19

Use implicit differentiation to find   . ​   ​

Accepted Answer

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

Question 20

Find the slope of the tangent line   at the given point   . Round your answer to two decimal places. ​

Accepted Answer

A)  0.67 
B)  2.00 
C)  1.00 
D)  1.67 
E)  3.00 
A)  0.67 
B)  2.00 
C)  1.00 
D)  1.67 
E)  3.00

Complete two iterations of Newton's Method for the function using the initial guess 2.2. Round your answers to four decimal places.

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

Find the derivative of the function.

Find the slope of the line tangent to the graph of the function at the point .

Use the general rule to approximate and to three decimal places. ,

Find the derivative of the function.

Find the derivative of the function.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when .

Use implicit differentiation to find at the point .

Find if .

Approximate the fixed point of the function between and to two decimal places. [A fixed point of a function f is a value of x such that .]

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place.

Use the Product Rule to differentiate.

Find the derivative of the algebraic function .

Find an equation to the tangent line for the graph of f at the given point. ,

The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.

Find the slope of the graph of the function at the given value. when

Use implicit differentiation to find .

Find the slope of the tangent line at the given point . Round your answer to two decimal places.

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

Complete two iterations of Newton's Method for the function using the initial guess 2.2. Round your answers to four decimal places. ​

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

Find the derivative of the function. ​ ​

Find the slope of the line tangent to the graph of the function at the point . ​

Use the general rule to approximate and to three decimal places. ​ , ​

Find the derivative of the function. ​ ​

Find the derivative of the function. ​ ​

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when . ​

Use implicit differentiation to find at the point . ​ ​

Find if . ​

Approximate the fixed point of the function between and to two decimal places. [A fixed point of a function f is a value of x such that .] ​

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place. ​

Use the Product Rule to differentiate. ​ ​

Find the derivative of the algebraic function . ​

Find an equation to the tangent line for the graph of f at the given point. ​ , ​

The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. ​

Find the slope of the graph of the function at the given value. ​ when ​

Use implicit differentiation to find . ​ ​

Find the slope of the tangent line at the given point . Round your answer to two decimal places. ​

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

Complete two iterations of Newton's Method for the function using the initial guess 2.2. Round your answers to four decimal places.

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

Find the derivative of the function.

Find the slope of the line tangent to the graph of the function at the point .

Use the general rule to approximate and to three decimal places. ,

Find the derivative of the function.

Find the derivative of the function.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1,366 feet tall. Find the instantaneous velocity of the coin when .

Use implicit differentiation to find at the point .

Find if .

Approximate the fixed point of the function between and to two decimal places. [A fixed point of a function f is a value of x such that .]

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 7 seconds. Round your answer to one decimal place.

Use the Product Rule to differentiate.

Find the derivative of the algebraic function .

Find an equation to the tangent line for the graph of f at the given point. ,

The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.

Find the slope of the graph of the function at the given value. when

Use implicit differentiation to find .

Find the slope of the tangent line at the given point . Round your answer to two decimal places.