practice final exam - uh · practice final exam question 1 the following table of values gives a...

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Practice Final Exam

Question 1

The following table of values gives a company's annual profits in millions of dollars. Rescale the data so that the year 2003 corresponds to x = 0.

Find the cubic regression model for the data. Which of these is the coefficient of the x2 term of the cubic regression model?

a) -0.3647

b) 2.4071

c) 0.05

d) -0.6841

e) -2.7429

f) None of the above.

Question 2


Find the R2 value for the cubic regression model.

a) 0.99

b) 0.88

Year 2003 2004 2005 2006 2007 2008

Profits (in millions of dollars) 51.7 53.2 51.9 52.2 56.1 58.3

Year 2001 2002 2003 2004 2005 2006


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12/3/2012https://assessment.casa.uh.edu/Assessment/PrintTest.htm

c) 0.94

d) 0.95

e) 0.90


Question 3


Find the exponential regression model for this data.

a)

b)

c)

d)

e)

f)

g) None of the above.

Question 4

Evaluate the limit:

a) 7

b)

Year 2003 2004 2005 2006 2007 2008


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c) -3

d) 0

e)


Question 5

Evaluate the limit:

a) 1⁄4

b) -1⁄4

c) 0

d) -4

e) Does not exist


Question 6

Find the indicated limit (if it exists).

a) Does not exist

b) 0

c) 20

d) -10

e) -20


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Question 7

Find the indicated limit (if it exists)

a) 10⁄

3

b) 2

c) Does not exist

d) -2

e) 0


Question 8

Find the indicated limit (if it exists).

a) 9

b) 7⁄2

c) -1⁄2

d) 10⁄3

e) ∞


Question 9

Find

using the graph of f(x) given below.

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a) 0

b) -5

c) 2

d) Does not exist.

e) None of the above.

Question 10

The graph of the function f is given below. Which of the following statements is true?

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a) The function is continuous at x = 2.

b) The function is discontinuous at x = 2 because f (2) does not exist.

c) The function is discontinuous at x = 2 because

does not exist.

d) The function is discontinuous at x = 2 because even though f (2) exists and

exists, the two quantities are not equal.

e) None of the above.

Question 11

Find the derivative of

a)

b)

c)

d)

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e)


Question 12

Suppose

Find the average rate of change of f(x) with respect to x in the interval [6, 8].

a) 10

b) -7

c) 22

d) 5

e) 11


Question 13

Give the equation of the tangent line to the graph of

at the point where x = 3.

a)

b)

c)

d)

e)


Question 14

A manufacturer has a monthly fixed cost of $270,000.00 and a production cost of $48 for each unit

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produced. The product sells for $72 per unit. Find the break-even quantity.

a) 3,750

b) 810,000

c) 6,000

d) 11,250

e) 2,250


Question 15

A leading producer of airplanes finds that the company's weekly cost of manufacturing x airplanes is given by the function

where C(x) is given in thousands of dollars. Use the marginal cost function to approximate the cost

of producing the 3,001st airplane.

a) $5,100,697.00

b) $5,100,700.00

c) $5,100,701.00

d) $5,100.70

e) $5,104.70


Question 16

A computer company manufactures a certain variety of flat panel monitor. The demand for this

monitor is given by the following equation, where p denotes the unit price and x denotes the quantity demanded.

(0 ≤ x ≤ 5000)

Use the marginal revenue function to approximate the actual revenue realized on the sale of the

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1,000th monitor.

a) $304.00

b) $300.20

c) $302.20

d) $304.20

e) $300.00


Question 17

A clothing company manufactures a certain variety of ski jacket. The total cost of producing x ski

jackets and the total revenue of selling x ski jackets are given by the following equations

(0 ≤ x ≤ 1000)

Use the marginal profit to approximate the actual profit realized on the sale of the 901st ski jacket.

a) $65.00

b) $63.00

c) $62.00

d) $64.00

e) $66.00


Question 18

A company manufactures LED televisions. The total cost of producing x LED televisions can be approximated by the function

Find the average cost of producing 120 LED televisions.

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a) $700.40 per player

b) $702.40 per player

c) $698.40 per player

d) $701.40 per player

e) $704.40 per player


Question 19

Suppose the demand function for a product is given by

p = -0.05x + 200

where the function gives the unit price in dollars when x units are demanded. Compute the elasticity of demand, E(p), when the price is $100.

a) 1.00

b) 0.75

c) 0.14

d) 0.85

e) 1.24


Question 20

Suppose E(p) = 2⁄3 when the price of the item is p. Then the demand is

a) Elastic

b) Unitary

c) Inelastic

d) None of the above.

Question 21

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If Q(t) = 18.1 e-0.0417t , find Q(t) when t = 4.

a) 61.2771

b) 21.3855

c) 15.3193

d) -2.5553

e) -0.6388


Question 22

At the beginning of an experiment, a researcher has 511 grams of a substance. If the half-life of the substance is 18 days, how much of the substance is left after 18 days?

a) 28.39 grams

b) 255.50 grams

c) 0 grams

d) 56.78 grams

e) Not enough information is given to answer.


Question 23

At the beginning of an experiment, a researcher has 523 grams of a substance. If the half-life of the substance is 16 days, how many grams of the substance are left after 29 days?

a) 74.45

b) 918.52

c) 0

d) 148.90

e) 1837.04

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Question 24

The demand for a company's product t months after it is introduced on the market can be expressed as

where D(t) is the number demanded. How many units should the company expect to be demanded when it is first introduced on the market?

a) 4,000

b) 3,825

c) 105

d) 1,500

e) 0


Question 25

Suppose

Which of these statements is/are true?

I. The domain of the function is not (-∞ , ∞).

II. The range of the function is not (-∞ , ∞). III. The graph of the function has no asymptotes.

IV. The y-intercept is (0, -10).

a) Only II and III are true.

b) All of the statements are true.

c) None of the statements are true.

d) Only II, III and IV are true.

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e) Only I, II and IV are true.

f) Only I and III are true.

Question 26

Find the critical numbers:

a) x = -20.99, 10.60

b) x = -3.45, -12.21

c) x = 2.09, -1.02

d) x = 0.54

e) x = -2.09, 1.02


Question 27

The graph shown below is the graph of the first derivative of a function, f (x). State the number of inflection points and the number of relative minima.

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a) 3 and 3

b) 2 and 2

c) 3 and 1

d) 3 and 2

e) 2 and 3

Question 28

Suppose

Find any critical numbers.

a) -0.4082, 0.4082

b) 0

c) -0.7071, 0, 0.7071

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d) -0.7071, 0.7071

e) -0.4134, 0.4134


Question 29

Suppose

Find intervals on which the function is increasing and intervals on which the function is decreasing.

a) Increasing on (-0.4082, 0.4082) ; decreasing on (-∞, -0.4082) ∪ (0.4082, ∞)

b) Increasing on (-∞, -0.4082) ∪ (0.4082, ∞) ; decreasing on (-0.4082, 0.4082)

c) Increasing on (-∞, -0.4134) ∪ (0.4134, ∞) ; decreasing on (-0.4134, 0.4134)

d) Increasing on (0, ∞) ; decreasing on (-∞, 0)

e) Increasing on (-0.4134, 0.4134) ; decreasing on (-∞, -0.4134) ∪ (0.4134, ∞)


Question 30

Suppose

Find any relative extrema.

a) Relative maximum at (0.3536, 0.1072); relative minimum at (-0.3536, -0.1072)

b) Relative maximum at (-0.3536, -0.1072); relative minimum at (0.3536, 0.1072)

c) Relative maximum at (0.3783, 0.1067); relative minimum at (-0.3783, -0.1067)

d) Relative maxima at (-0.6124, -0.0683) and (0.6124, 0.0683); relative minimum at (0, 0)

e) Relative maximum at (0, 0); relative minima at (-0.6124, -0.0683) and (0.6124, 0.0683)

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Question 31

Suppose

Find any values of x for which f'' ( x ) = 0.

a) x = -0.4082, x = 0, x = 0.4082

b) x = -0.7071, x = 0, x = 0.7071

c) x = -0.7071, x = 0.7071

d) x = -0.7165, x = 0.7165

e) x = 0


Question 32

Suppose

Find intervals on which the function is concave upward and intervals on which it is concave downward.

a) Concave upward on (-∞, -0.6124) ∪ (0, 0.6124) ; concave downward on (-0.6124, 0) ∪

(0.6124, ∞)

b) Concave upward on (-0.6124, 0) ∪ (0.6124, ∞) ; concave downward on (-∞, -0.6124) ∪ (0,

0.6124)

c) Concave upward on (-0.3536, 0.3536) ; concave downward on (-∞, -0.3536) ∪ (0.3536, ∞)

d) Concave upward on (0, ∞) ; concave downward on (-∞, 0)

e) Concave upward on (-∞, 0) ; concave downward on (0, ∞)

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Question 33

Suppose

Find any inflection points.

a) (-0.3162, -0.0959), (0, 0), and (0.3162, 0.0959)

b) (-0.5477, -0.0611) and (0.5477, 0.0611)

c) (-0.5477, -0.0611), (0, 0), and (0.5477, 0.0611)

d) (-0.3162, -0.0959) and (0.3162, 0.0959)

e) (-0.3353, -0.0956) and (0.3353, 0.0956)


Question 34

Suppose

Find any asymptotes.

a) No horizontal asymptotes ; vertical asymptote at x = 0.

b) Horizontal asymptote at y = 1 ; no vertical asymptotes.

c) Horizontal asymptote at y = 0 ; no vertical asymptotes.

d) Horizontal asymptote at y = 1 ; vertical asymptote at x = 0.

e) Horizontal asymptote at y = 0 ; vertical asymptote at x = 0.


Question 35

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The graph of a function, f (x) , is given below. Find the absolute maximum value of this function.

a) 1

b) -1

c) 0

d) -2

e) 2


Question 36

Suppose you want to fence in a rectangular-shaped field that lies along the straight edge of a river. The side that lies along the river will not need to be fenced. You have 500 feet of fencing material to use. Which of these is a function that expresses the area of the field that can be fenced in under these conditions, where x is the length of one of the two sides of the field that are perpendicular to the river?

a) A (x) = x (250 − x)

b) A (x) = x (500 − x)

c) A (x) = x (250 − 2x)

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d) A (x) = x (500 − 2x)

e) A (x) = x (250x − x2)


Question 37

Suppose you want to fence in a rectangular-shaped field that lies along the straight edge of a river. The side that lies along the river will not need to be fenced. You have 250 feet of fencing material to use. What is the maximum area that can be fenced in under these conditions?

a) 11718.7500

b) 1157.4074

c) 15625

d) 3906.2500

e) 7812.5000


Question 38

Let f (x) = 4x2 + 4 . Compute the Riemann sum of f over the interval [0, 4] using 4 subintervals, choosing the left endpoints of the subintervals as representative points.

a) 100

b) 72

c) 60

d) 140

e) 136


Question 39

Use Riemann sums with right endpoints and 20 subdivisions to approximate the area between

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and the x-axis on the interval [1, 5]. Round the answer to the nearest ten-thousandth.

a) 12.4924

b) 12.3301

c) 11.6699

d) 17.3121

e) 12.4032


Question 40

Find the indefinite integral

a)

b)

c)

d)

e)


Question 41

Evaluate

a) -738

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b) 261⁄2

c) -234

d) -198

e) -774


Question 42

An efficiency study showed that the rate at which the average worker assembles products t hours after starting work can be modeled by the function

where 0 ≤ t ≤ 4. Determine the number of units the average worker can assemble during the third hour that s/he works during a shift.

a) 16 units

b) 42 units

c) 123 units

d) 111 units

e) 4 units


Question 43

Suppose the velocity of a car can be modeled by the function

where t is time given in seconds and v(t) is given in feet per second. Find the total distance traveled by the car from t = 0 to t = 3.

a) 1269.00 feet

b) 26.52 feet

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c) 11.29 feet

d) 180.04 feet

e) 12.59 feet


Question 44

A company estimates that its annual sales during the first t years of operation can be modeled by the function

where S is measured in thousands of dollars. What was the company's average annual sales over its first 3 years of operation?

a) $19.21 thousand

b) $5.59 thousand

c) $2.78 thousand

d) $8.35 thousand

e) $6.40 thousand


Question 45

Find the area of the region between f (x) = x2 − 9x and g (x) = 6x.

a) 58.5000

b) -364.5000

c) -562.5000

d) 364.5000

e) 562.5000


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Question 46

Find the area of the region(s) that is/are completely enclosed by the graphs of

f ( x ) = ( x − 1 )3 + 1

and

g ( x ) = 3x − 3

Round limits of integration to 4 decimal places before integrating.

a) 0.7814

b) 4.2286

c) 5.0100

d) 3.4472

e) 1.6700


Question 47

Let

Find f ( -7, 8).

a) 46

b) 60

c) -448

d) -564

e) -444


Question 48

Find the critical points of

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a) ( 0 , 0 ) , ( 1⁄18 , 1⁄54 )

b) ( 0 , 0 ) , ( -1⁄18

, -1⁄54

)

c) ( 1⁄18

, 1⁄108

)

d) ( 0 , 0 )

e) ( 0 , 0 ) , ( 1⁄18 , 1⁄108 ) , ( 0 , 1⁄108 ) , ( 1⁄18 , 0 )


Question 49

Suppose fxx = 18x , fyy = 8 , fxy = fyx = − 5

and the critical points for function f are

A = (0.6760, 0.4225) and B = (-0.3287, -0.2055)

Find the value for D for each critical point and then classify the critical point using the second derivative test.

a) D(0.6760, 0.4225) = 72.3440 ; relative maximum at (0.6760, 0.4225) ; D(-0.3287, -0.2055)

= -72.3328 ; saddle point at (-0.3287, -0.2055)

b) D(0.6760, 0.4225) = 122.3440 ; relative maximum at (0.6760, 0.4225) ; D(-0.3287, -0.2055)

= -22.3328 ; saddle point at (-0.3287, -0.2055)

c) D(0.6760, 0.4225) = 72.3440 ; saddle point at (0.6760, 0.4225) ; D(-0.3287, -0.2055) = -

72.3328 ; relative minimum at (-0.3287, -0.2055)

d) D(0.6760, 0.4225) = 72.3440 ; relative minimum at (0.6760, 0.4225) ; D(-0.3287, -0.2055) =

-72.3328 ; saddle point at (-0.3287, -0.2055)

e) D(0.6760, 0.4225) = 122.3440 ; relative minimum at (0.6760, 0.4225) ; D(-0.3287, -0.2055)

= -22.3328 ; saddle point at (-0.3287, -0.2055)


Question 50

Suppose that

f ( x , y ) = 4 x 3 − 7 x y + 8 y 2 ,

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(0.2552 , 0.1117) is a critical point,

f xx

| (0.2552 , 0.1117)

= 6.1250 , and

D (0.2552 , 0.1117) = 49 .

Which of these statements describes the graph of f at (0.2552 , 0.1117) ?

a) f has a relative minimum value at f (0.2552 , 0.1117) = 0.1662.

b) f has a saddle point at f (0.2552 , 0.1117) = -0.0332.

c) f has a relative minimum value at f (0.2552 , 0.1117) = -0.0332.

d) f has a relative maximum value at f (0.2552 , 0.1117) = 0.1662.

e) f has a relative maximum value at f (0.2552 , 0.1117) = -0.0332.

f) f has a saddle point at f (0.2552 , 0.1117) = 0.1662.

g) None of the above.

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practice final exam - uh · practice final exam question 1 the following table of values gives a...

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