Deck 11: Mathematical Functions and Limits

Question 1

Use the four step process to find f'(x) for the function https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/.

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

Answer 1

10x +5h-3

Question 2

Answer 2

C

Question 3

Answer 3

C

Question 4

f(x) =

A)10-3x
B) -6x
C) 10-6x
D)

Question 5

Is f continuous at x = 0?

A)Yes
B)No

Question 6

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

Question 7

Use the graph of f given below to find f(-10).

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

Question 8

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

Question 9

Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function y =

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

Question 10

Is f continuous at x = 0?

A)No
B)Yes

Question 11

Question 12

Find: lim x·- 4

A)- 24
B)8
C)16
D)-8

Question 13

f(x) =

A)
B)
C)
D)

Question 14

Is f continuous at x = -0.5?

A)Yes
B)No

Question 15

Determine the limit.

A)-2
B)œ
C)-œ
D)5

Question 16

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?

Question 17

Question 18

C(x).

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

Question 19

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

Question 20

Question 21

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

Question 22

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

Question 23

If an object moves along a line so that it is at y = f(x) = 10x² 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 24

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

Question 25

Find f'(x) for f(x) =

A)
B)
C)
D)

Question 26

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

Question 27

Suppose an object moves along the y-axis so that its location is y = f(x) = x² + x 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 28

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

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

Question 29

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

Question 30

Find f'(x) if f(x) =

A)
B)
C)
D)

Question 31

Suppose an object moves along the y-axis so that its location is y = f(x)= x² + x at time x (y is in meters and x is in seconds). Find the average veloity for x changing from 3to 3 + h seconds.

A) 7-h m/s
B) 12+h m/s
C) 12-h m/s
D) 7 +h m/s

Question 32

Find y' if y = 6x.

Question 33

Suppose an object moves along the y-axis so that its location is y = f(x) = 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 34

The electric power p (in W) as a function of the current i (in A) in a certain circuit is given by p(i) = https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/.
Find the instantaneous rate of change of p with respect to i for i = 0.6 A.

A) 56 W/A
B) 42 W/A
C) 62 W/A
D) 33.6 W/A

Question 35

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

Question 36

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 37

Find f'(x) if

A)
B)
C)
D)

Question 38

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 39

Find f'(x) if f(x) =n.

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

Question 40

Find the derivative of

A)
B)
C)
D)

Question 41

The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000 +90x - Find the marginal
average cost at x = 20, and interpret the result.

A) -$10.33; a unit increase in produuction 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 at a
production level of 20 units.
C)-$1.33; unit increase in prodction 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 42

Question 43

A)
B)
C)
D)

Question 44

Question 45

Find the equation of the tangent line at x = 7 for f(x) = 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 46

y = 2x + 3; x = 18,6x = 0.5

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

Question 47

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

A)
B) D'(p)=-8p+3
C) D'(p)=-4p+3
D)

Question 48

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 49

y=

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

Question 50

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 51

Question 52

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: 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 53

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

Question 54

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.

Question 55

Question 56

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 57

An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by (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 58

A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by:
0 c x c 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.