Deck 9: Markov Chains

Question 1

Find the limit, if it exists
Find:

A)-1
B)1
C)0
D)Does not exist

Answer 1

-1

Question 2

Sketch a possible graph of a function that satisfies the given conditions.
f(0) = -3 and

A)
B)
C)
D)

Answer 2

Question 3

Find average rate of change for the function over the given interval.
Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y = x² + 3x.

A)22
B)4
C)9
D)11

Answer 3

11

Question 4

Provide an appropriate response.
Use a sign chart to solve the inequality. Express answers in interval notation.

A)
B)
C)
D) (-4, 4)

Question 5

Solve the problem.
The cost of renting a snowblower is $20 for the first hour (or any fraction thereof)and $5 for each additional hour (or fraction thereof)up to a maximum rental time of 5 hours.Write a piecewise definition of the cost C(x)of renting a snowblower for x hours.Is C(x)continuous at x = 2.5?

A)
B)
C)
D)

Question 6

Sketch a possible graph of a function that satisfies the given conditions.
f(-1) = -7 ;

A)
B)
C)
D)

Question 7

The graph of y = f(x) is shown. Use the graph to answer the question.
Is f continuous at x = -0.5?

A)Yes
B)No

Question 8

The graph of y = f(x) is shown. Use the graph to answer the question.
Is f continuous at x = 0?

A)No
B)Yes

Question 9

Use the definition f'(x) = to find the derivative at x.
f(x) = 10 - 3x²

A) 10-3x
B) -6x
C) 10-6x
D) -6x²

Question 10

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

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

Question 11

The graph of y = f(x) is shown. Use the graph to answer the question.
Is f continuous at x = 0?

A)Yes
B)No

Question 12

Provide an appropriate response.
Use a graphing utility to find the discontinuites of the given rational function.

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

Question 13

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).

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

Question 14

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

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

Question 15

Provide an appropriate response.

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

Question 16

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.

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

Question 17

Find the limit.
Determine the limit.

A)-2
B)∞
C)-∞
D)5

Question 18

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

A)
B)
C)
D)

Question 19

Find the instantaneous rate of change for the function at the value given.
Find the instantaneous rate of change for the function x² + 6x at x = 3.

A)27
B)9
C)6
D)12

Question 20

Solve the problem.
The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The average cost per tape, denoted by , is found by dividing C(x) by x. Find

A)14
B)10
C)6
D)Does not exist

Question 21

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

A)
B)
C)
D)

Question 22

List the x-values in the graph at which the function is not differentiable.

A)x = 2
B)x = -2,x = 2
C)x = 0
D)x = -2,x = 0,x = 2

Question 23

Provide an appropriate response.
y = x⁴ + 2x³ + 2x + 2 at x = -3

A)65
B)-52
C)67
D)-50

Question 24

Solve the problem.
Suppose an object moves along the y-axis so that its location is at time x (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.

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

Question 25

Solve the problem.
If an object moves along a line so that it is at at time x (in seconds), find the instantaneous velocity function v = f'(x).

A)
B) 6x+7
C)
D) 3x+7

Question 26

Suppose an object moves along the y-axis so that its location is y = at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

A) 8 m/s
B) 9 m/s
C) 20 m/s
D) 10 m/s

Question 27

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

A)
B)
C)
D)

Question 28

Provide an appropriate response.
Let f and g be functions that satisfy f'(4)= 2 and g'(4)= -3.Find h'(4)for h(x)= 3f(x)- g(x)+ 2.

A)5
B)2
C)11
D)9

Question 29

Provide an appropriate response.
Find the derivative of

A)
B)
C)
D)

Question 30

Provide an appropriate response.
Given f(x + h) - f(x) = 4xh + 4h + 2h², find the slope of the tangent line at x = 4.

A)20
B)8
C)22
D)16

Question 31

List the x-values in the graph at which the function is not differentiable.

A)x = -2,x = 2
B)x = -3,x = 0,x = 3
C)x = -3,x = 3
D)x = -2,x = 0,x = 2

Question 32

Provide an appropriate response.
Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for f(x) = -3x² - 8.

A)-55
B)15
C)-15
D)55

Question 33

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

A) f'x=0
B) f'(x)=1
C) f'x=π
D) f'(x) = π2

Question 34

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).

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

Question 35

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.

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

Question 36

List the x-values in the graph at which the function is not differentiable.

A)x = 2
B)x = 0
C)x = 1
D)x = -1

Question 37

Provide an appropriate response.
Find

A)
B)
C)
D)

Question 38

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

A)
B)
C)
D)

Question 39

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

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

Question 40

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.

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

Question 41

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.

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

Question 42

Provide an appropriate response.

A)y = 216x + 54
B)y = 54x + 216
C)y = 18x + 216
D)y = 216x + 18

Question 43

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.

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

Question 44

Provide an appropriate response.
Evaluate dy and for y = f(x) = 20+ x = 2, and dx = = 0.3.

A) dy = 14.4; = 14.4
B) dy = 14.4; =15.183
C) dy= = 5.183; =15.183
D) dy= = 5.183; =14.4

Question 45

Solve the problem.
The demand equation for a certain item is and the cost equation is C(x) = 7,000 + 4x. Find the marginal profit at a production level of 3,000 and interpret the result.

A)$14; at the 3,000 level of production,profit will increase by approximately $14 for each unit increase in production.
B)$16; at the 3,000 level of production,profit will increase by approximately $16 for each unit increase in production.
C)$7; at the 3,000 level of production,profit will increase by approximately $7 for each unit increase in production.
D)$4; at the 3,000 level of production,profit will increase by approximately $4 for each unit increase in production.

Question 46

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.

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

Question 47

Provide an appropriate response.
Find the equation of the tangent line at x = 2 for Write the answer in the form y =mx+b.

A) y=-43x+48
B) y=-47x +68
C) y=-43x +60
D) y=-39x +52

Question 48

Provide an appropriate response.

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

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

Question 49

Find dy.
y=

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

Question 50

Solve the problem.
According to one theory of learning,the number of items,w(t),that a person can learn after t hours of instruction is given by: 0 ≤ t ≤ 64 Find the rate of learning at the end of eight hours of instruction.

A)20 items per hour
B)60 items per hour
C)5 items per hour
D)45 items per hour

Question 51

Provide an appropriate response.
The total cost in dollars of producing x lawn mowers is given by C(x) = Find the marginal
average cost at x = 20, and interpret the result.

A) -$10.33; a unit increase in production will decrease the average cost per unit by approximately $10.33 ata
production level of 20 units.
B) -$13.33; a unit increase in production will decrease the average cost per unit by approximately $13.33 ata
production level of 20 units.
C)-$1.33; a unit increase in production will decrease the average cost per unit by approximately $1.33 at a
production level of 20 units.
D) -$20.33; a unit increase in production will decrease the average cost per unit by approximately $20.33 at a
production level of 20 units.

Question 52

Solve the problem.
A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by:
c(x)= 0 ≤ x ≤ 100
Find the marginal cost at a production level of 70 dozen pens and interpret the result.

A) The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen
pens is approximately $0.60.
B) The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen
pens is approximately $0.59.
C) The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen
pens is approximately $0.62.
D) The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen
pens is approximately $0.58.

Question 53

Find dy.
Find dy.
y=

A)
B)
C)
D)

Question 54

Solve the problem.
Suppose the demand for a certain item is given by where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price.

A)
B)
C)
D)

Question 55

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

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

Question 56

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

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

Question 57

Solve the problem.
A company is planning to manufacture a new blender.After conducting extensive market surveys,the research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per blender.Assuming the demand equation is linear,use the research department's estimates to find the revenue equation in terms of the demand x.

A)
B)
C)
D)

Question 58

Provide an appropriate response.
Find the values of x where the tangent line is horizontal for f(x) = 3x³ - 2x² - 9.

A)
B)
C)
D)