Question 1

Find Δy for the given values of xS1U1B11S1U1B0 and xS1U1B12S1U1B0.
-y = 2x + 3; x = 18,Δx = 0.5

Accepted Answer

A) 0.5 
B) 5 
C) 1 
D) 0.1 
A) 0.5 
B) 5 
C) 1 
D) 0.1

Question 2

Provide an appropriate response.
-Find f'(x) for f(x) =

Accepted Answer

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

Question 3

Provide an appropriate response.
-Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=4x2 - 5x + 10.Find the marginal profit at x = 5.

Accepted Answer

A) $45 
B) $15 
C) $35 
D) $32 
A) $45 
B) $15 
C) $35 
D) $32

Question 4

Provide an appropriate response.
-

Accepted Answer

A)  3 
B)  1 
C)  -1 
D)  Continuous at all values of x 
A)  3 
B)  1 
C)  -1 
D)  Continuous at all values of x

Question 5

Provide an appropriate response.
-Use the four step process to find f'(x) for the function f(x) = 5x2 - 3x.

Accepted Answer

A)  5h-3 
B)  10x-3 
C)  10x +5h-3 
D)  5h2 - 3h 
A)  5h-3 
B)  10x-3 
C)  10x +5h-3 
D)  5h2 - 3h

Question 6

Solve the problem.
-A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where P(x) =   Find

Accepted Answer

A) 105 
B) 30 
C) 42 
D) Does not exist 
A) 105 
B) 30 
C) 42 
D) Does not exist

Question 7

Solve the problem.
-An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by
f(t)=   Find the velocity at three seconds.

Accepted Answer

A)  197 feet per second 
B)  192 feet per second 
C)  109 feet per second 
D)  190 feet per second 
A)  197 feet per second 
B)  192 feet per second 
C)  109 feet per second 
D)  190 feet per second

Question 8

Find the instantaneous rate of change for the function at the value given.
-Find the instantaneous rate of change for the function f(x) = 5x2 + x at x = - 4.

Accepted Answer

A) -14 
B) -41 
C) 6 
D) -39 
A) -14 
B) -41 
C) 6 
D) -39

Question 9

Use the definition f'(x) =   to find the derivative at x.
-

Accepted Answer

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

Question 10

Provide an appropriate response.
-Find the equation of the tangent line at x = 7 for   Write the answer in the form y = mx +b.

Accepted Answer

A)  y=-2x 
B)  y=-14x+55 
C)  y=14x-55 
D)  y=7x+55 
A)  y=-2x 
B)  y=-14x+55 
C)  y=14x-55 
D)  y=7x+55

Question 11

Provide an appropriate response.
-Find the derivative of

Accepted Answer

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

Question 12

Solve the problem.
-If an object moves along a line so that it is at y = f(x) =   at time x (in seconds), find the velocity at x = 1 (y is measured in feet).

Accepted Answer

A)  20 ft/s 
B)  10 ft/s 
C)  6 ft/sec 
D)  200 ft/s 
A)  20 ft/s 
B)  10 ft/s 
C)  6 ft/sec 
D)  200 ft/s

Question 13

Provide an appropriate response.
-Find f'(x) if f(x) =

Accepted Answer

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

Question 14

The graph of a function f is given. Use the graph to answer the question.
-Use the graph of f given below to find f(-10).

Accepted Answer

A) 16 
B) -10 
C) 0 
D) 6 
A) 16 
B) -10 
C) 0 
D) 6

Question 15

Solve the problem.
-The electric power p (in W) as a function of the current i (in A ) in a certain circuit is given by  
Find the instantaneous rate of change of p with respect to i for i = 0.6 A.

Accepted Answer

A)  56 WA 
B)  2 W/A 
C)  62 W/A 
D)  33.6 W/A 
A)  56 WA 
B)  2 W/A 
C)  62 W/A 
D)  33.6 W/A

Question 16

Provide an appropriate response.
-The revenue (in thousands of dollars) from producing x units of an item is modeled Rb(yx) =  
Find the marginal revenue at x = 1000.

Accepted Answer

A)  $104.00 
B)  $10,300.00 
C)  $4.00 
D)  $4.50 
A)  $104.00 
B)  $10,300.00 
C)  $4.00 
D)  $4.50

Question 17

Provide an appropriate response.

-Evaluate dy and   for  y =f(x)= -7x + 5, x = 7, and dx =   = 0.5.

Accepted Answer

A)  dy = 3.75;   =35 
B)  dy = 3.75;   = 375 
C)  dy = 3.5;   = 3.75 
D)  dy = 3.5;   = 3.5 
A)  dy = 3.75;   =35 
B)  dy = 3.75;   = 375 
C)  dy = 3.5;   = 3.75 
D)  dy = 3.5;   = 3.5

Question 18

Solve the problem.
-Suppose an object moves along the y-axis so that its location is y =   (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

Accepted Answer

A)  84 m/s 
B)  12 m/s 
C)  15 m/s 
D)  3 m/s 
A)  84 m/s 
B)  12 m/s 
C)  15 m/s 
D)  3 m/s

Question 19

Provide an appropriate response.
-Find the slope of the graph f(x) = -x2 + 3x at the point (1, 2).

Accepted Answer

A) -2 
B) -1 
C) 2 
D) 1 
A) -2 
B) -1 
C) 2 
D) 1

Question 20

Find dy.
-y=

Accepted Answer

A)  18x dx 
B)  (18x +9) dx 
C)  18x +18 dx 
D)  18x - 3 dx 
A)  18x dx 
B)  (18x +9) dx 
C)  18x +18 dx 
D)  18x - 3 dx

Find Δy for the given values of x₁ and x₂. -y = 2x + 3; x = 18,Δx = 0.5

Provide an appropriate response. -Find f'(x) for f(x) =

Provide an appropriate response. -Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=4x2 - 5x + 10.Find the marginal profit at x = 5.

Provide an appropriate response. -

Provide an appropriate response. -Use the four step process to find f'(x) for the function f(x) = 5x² - 3x.

Solve the problem. -A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where P(x) = Find

Solve the problem. -An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by f(t)= Find the velocity at three seconds.

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function f(x) = 5x² + x at x = - 4.

Use the definition f'(x) = to find the derivative at x. -

Provide an appropriate response. -Find the equation of the tangent line at x = 7 for Write the answer in the form y = mx +b.

Provide an appropriate response. -Find the derivative of

Solve the problem. -If an object moves along a line so that it is at y = f(x) = at time x (in seconds), find the velocity at x = 1 (y is measured in feet).

Provide an appropriate response. -Find f'(x) if f(x) =

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(-10).

Solve the problem. -The electric power p (in W) as a function of the current i (in A ) in a certain circuit is given by Find the instantaneous rate of change of p with respect to i for i = 0.6 A.

Provide an appropriate response. -The revenue (in thousands of dollars) from producing x units of an item is modeled Rb(yx) = Find the marginal revenue at x = 1000.

Provide an appropriate response. -Evaluate dy and for y =f(x)=-7x + 5, x = 7, and dx = = 0.5.

Solve the problem. -Suppose an object moves along the y-axis so that its location is y = (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

Provide an appropriate response. -Find the slope of the graph f(x) = -x² + 3x at the point (1, 2).

Find dy. -y=

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Exam 9: Markov Chains

Find Δy for the given values of x1 and x2. -y = 2x + 3; x = 18,Δx = 0.5

Provide an appropriate response. -Find f'(x) for f(x) =

Provide an appropriate response. -Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=4x2 - 5x + 10.Find the marginal profit at x = 5.

Provide an appropriate response. -

Provide an appropriate response. -Use the four step process to find f'(x) for the function f(x) = 5x2 - 3x.

Solve the problem. -A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where P(x) = Find

Solve the problem. -An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by f(t)= Find the velocity at three seconds.

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function f(x) = 5x2 + x at x = - 4.

Use the definition f'(x) = to find the derivative at x. -

Provide an appropriate response. -Find the equation of the tangent line at x = 7 for Write the answer in the form y = mx +b.

Provide an appropriate response. -Find the derivative of

Solve the problem. -If an object moves along a line so that it is at y = f(x) = at time x (in seconds), find the velocity at x = 1 (y is measured in feet).

Provide an appropriate response. -Find f'(x) if f(x) =

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(-10).

Solve the problem. -The electric power p (in W) as a function of the current i (in A ) in a certain circuit is given by Find the instantaneous rate of change of p with respect to i for i = 0.6 A.

Provide an appropriate response. -The revenue (in thousands of dollars) from producing x units of an item is modeled Rb(yx) = Find the marginal revenue at x = 1000.

Provide an appropriate response. -Evaluate dy and for y =f(x)=-7x + 5, x = 7, and dx = = 0.5.

Solve the problem. -Suppose an object moves along the y-axis so that its location is y = (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

Provide an appropriate response. -Find the slope of the graph f(x) = -x2 + 3x at the point (1, 2).

Find dy. -y=

Linear Equations and Graphs

Mathematics of Finance

Linear Inequalities and Linear Programming

Logic, sets, and Counting

Probability

Limits and the Derivative

Mathematical Functions and Limits

Filters

Find Δy for the given values of x₁ and x₂. -y = 2x + 3; x = 18,Δx = 0.5

Provide an appropriate response. -Use the four step process to find f'(x) for the function f(x) = 5x² - 3x.

Find the instantaneous rate of change for the function at the value given. -Find the instantaneous rate of change for the function f(x) = 5x² + x at x = - 4.

Provide an appropriate response. -Find the slope of the graph f(x) = -x² + 3x at the point (1, 2).