Deck 15: Integration

Question 1

By using differentials,an approximation of is

A)
B)
C)
D)
E)

Answer 1

Question 2

Use differentials only to find an approximate value of
.

Answer 2

2.9962963

Question 3

By using differentials,an approximation of ln(1.03)is

A) -0.01.
B) 0.01.
C) 0.02.
D) 0.03.
E) 0.04.

Answer 3

0.03.

Question 4

If q =
- 6
+ 3p - 8,find
when p = 1.

Question 5

If y = ,then dy =

A) dx.
B) dx.
C) 6x dx.
D) dx.
E) dx.

Question 6

Use differentials to approximate: ln(0.95).

Question 7

If y =
,use differentials to approximate the change in y if x changes from 25 to 25.3.

Question 8

Use differentials and R = 300x+ 50
-
to approximate the change in revenue R (in dollars)from selling x pounds if the number of pounds increases from 10 to 10.2.

Question 9

If y = (
+ 3
,find
.

Question 10

Find dy if y =
.

Question 11

Use differentials to approximate:
.

Question 12

Find dy if y = (5
+
.

Question 13

Use differentials only to find an approximate value of
.

Question 14

Find the differential of the function in terms of x and dx.
y = ln(
- 3x + 1)

Question 15

Find the differential of the function in terms of x and dx.
y =

Question 16

Use differentials only to find an approximate value of
.

Question 17

Use differentials to approximate:

Question 18

If y = x ln x,then dy =

A) 1 + ln x.
B) (1 + ln x) dx.
C) x + ln x.
D) (x + ln x) dx.
E) none of the above

Question 19

Use differentials only to find an approximate value of
.

Question 20

Find dy if y =
.

Question 21

Use differentials to approximate
.

Question 22

Find the differential in terms of x and dx.
y =

Question 23

Use differentials to approximate
.

Question 24

The supply equation for a certain radio is given by p = 0.8
+ 17 where p is the price in dollars and x is the number of radios supplied.Use differentials to approximate the price when 620 radios are supplied.(Hint: Use x = 625.)

Question 25

The supply equation for a company is q =
.Find
from
.

Question 26

Scientists use the formula S =
to determine an animal's surface area S (in square meters)from its weight W (in kilograms),where k is a constant that varies from animal to animal.Suppose the scientist studies a certain animal with k = 0.3.Use differentials to approximate the surface area if the animal weighs 65 kilograms.(Hint: Use W = 64.)

Question 27

Use differentials and C = 250 + 0.30x to approximate the change in the cost C (in dollars)to produce x pounds of candy if the number of pounds of candy increases from 10 pounds to 10.6 pounds.

Question 28

The supply equation for a company is q = 4
+ 3.Find
from
.

Question 29

Find the differential in terms of x and dx.
y = 3
- 5x + 4

Question 30

Find the differential in terms of x and dx.
y = ln

Question 31

Find the differential in terms of x and dx.
y =

Question 32

Determine:

Question 33

Use differentials to approximate the change in the volume V of a sphere if the radius r is increased from 5 cm to 5.3 cm.(Hint: Use V =
π
.)

Question 34

The supply equation for a certain radio is given by p = 0.5
+ 12 where p is the price in dollars and x is the number of radios supplied.Use differentials to approximate the price when 1604 radios are supplied.(Hint: Use x = 1600.)

Question 35

Scientists use the formula S =
to determine an animal's surface area S (in square meters)from its weight W (in kilograms),where k is a constant that varies from animal to animal.Suppose the scientist studies a certain animal with k = 0.1.Use differentials to approximate the surface area if the animal weighs 124 kilograms.(Hint: Use W = 125.)

Question 36

Use differentials to approximate the change in the wattage W of a flood light with a resistance R = 8 ohms,if the current I is increased from 4 amperes to 4.2 amperes.(Hint: Use W =
.)

Question 37

The supply equation for a company is q = 4
- 2p.Find
from
.

Question 38

Use differentials to approximate ln(0.99).

Question 39

Use differentials to approximate
.

Question 40

The supply equation for a company is q = 0.5
- 3p.Find
from
.

Question 41

Determine:

Question 42

Determine:
dx

Question 43

Find the indefinite integral
dx.

Question 44

Determine:

Question 45

+ 2 dx =

A) 3 - + C
B) 3 + 4 + C
C) - + 2x + C
D) + + 2x+ C
E) - + 2x+ C

Question 46

dx =

A) -2x + C
B) 4 - 2x + C
C) - + 3x + C
D) 5 - 3 + 3x + C
E) + C

Question 47

Determine:
dx

Question 48

Find the indefinite integral
+
dx.

Question 49

Find the indefinite integral
dx.

Question 50

dx =

A) x + C
B) ∙ + C
C) ∙ + C
D) 0 + C
E) 0

Question 51

Find the indefinite integral
dx.

Question 52

Determine:
dx

Question 53

dx =

A) + C
B) + C
C) + C
D) + C
E) ( - x) + C

Question 54

Determine:

Question 55

Determine:

Question 56

Determine:
dp

Question 57

Find the indefinite integral

dx.

Question 58

Determine:

Question 59

Determine:

Question 60

Determine:
dx

Question 61

If y' = 6x - 3 and y(2)= 4,then y =

A) 6.
B) 3 - 3x.
C) 3 - 3x + 2.
D) 3 - 3x - 2.
E) 6 - 3x + 2.

Question 62

A manufacturer of a product has a marginal cost function given by where c is the total cost (in dollars)of producing q units of a product.If fixed costs are $30,000,then the total cost of producing 30 units is

A) $66,600.
B) $66,700.
C) $66,800.
D) $66,900.
E) $67,000.

Question 63

If the marginal revenue for a manufacturer's product is
= 700 - 6q - 8
,find the demand function.

Question 64

If = 3
- 3 and y(0)= 8,then y(1)=

A) 6.
B) 0.
C) 12.
D) 8.
E) 4.

Question 65

The marginal cost function for a manufacturer's product is given by
where c is in dollars.Find the cost function if fixed costs are $100.

Question 66

Determine:

Question 67

If the marginal cost for a company is f(x)= 6,find

Question 68

Determine:

Question 69

A manufacturer of a product has a marginal revenue function given by =200 + 70q - 3
)The demand function for the product is given by

A) p = - 6.
B) p = 70 - 6q.
C) p = 200q + 35 -
D) p = 200 + 35q -
E) p = 200q + 35 -

Question 70

For a group of rats that were fed a particular diet,the rate of change of the average weight gain G (in grams)of a rat with respect to the percent P of yeast in the diet is
If G = 36 when P = 8,find G.

Question 71

If y'' =
- 2,and y'(0)= 3 and y(0)= 4,find y.

Question 72

Determine

Question 73

Find y subject to the given conditions: y'' = 6x - 2; y'(1)= 2; y(1)= 2.

Question 74

Determine:

Question 75

The marginal cost function for a manufacturer's product is
= 0.0003
- 0.03q + 4,where c is in dollars.If fixed costs are $5000,determine: (a)the manufacturer's total cost function; (b)the manufacturer's average cost function.

Question 76

If the marginal revenue function for a manufacturer's product is
= 1000 - 10q - 6
,find the demand function.

Question 77

If
=
- 4x + 1 and y(3)= 8,find y.

Question 78

If y' = 6
- 4x - 3 and y(1)= 2,find y.

Question 79

Find y subject to the given conditions: y'' =

+ 5; y'(0)= 1; y(0)= 5

Question 80

If y'' = 6x + 2 and y'(1)= 2 and y(1)= 2,find y.