EVALUATING INTEGRALS. Evaluate the integral shown below. (Hint: Try the substitution u = (7x2 + 3).) 1) x dx (7x2 + 3)5 Evaluate the integral shown below. (Hint: Apply a property of logarithms first.) 2) ln x6 x dx 1 Use the Fundamental Theorem of Calculus to find the derivative shown below. 3) d dx x5 0 sin t dt For the function shown below, sketch a graph of the function, and then find the SMALLEST possible value and the LARGEST possible value for a Riemann sum of the function on the given interval as instructed. 4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of equal width. ^ CHARACTERISTICS and BEHAVIOR OF FUNCTIONS. Use l'Hopital's rule to find the limit below. 5) lim x 5x + 9 6x2 + 3x - 9 ^ Use l'Hopital's rule to find the limit below. (Hint: The indeterminate form is f(x)g(x).) 6) lim x 1 + 2 x3 x 2 Solve the following problem. 7) The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall. 9' wall 30' Hint: Let "h" be the height on the building where the ladder touches; let "x" be the distance on the ground between the wall and the foot of the ladder. Use similar triangles and the Pythagorean Theorem to write the length of the beam "L" as a function of "x". Also note that a radical function is minimized when it radicand is minimized. For the function shown below, identify its local and absolute extreme values (if any), saying where they occur. 8) f(x) = -x3- 9x2 - 24x + 3 3 Find a value for "c" that satisfies the equation f(b) - f(a) b - a = f (c) in the conclusion of the Mean Value Theorem for the function and interval shown below. 9) f(x) = x + 75 x , on the interval [3, 25] DERIVATIVES. Find the equation of the tangent line to the curve whose function is shown below at the given point. 10) x5y5 = 32, tangent at (2, 1) Use implicit differentiation to find dy/dx. 11) xy + x + y = x2y2 Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x). 12) y = u(u - 1), u = x2 + x 4 Find y . 13) y = (4x - 5)(4x3 - x2 + 1) Find the derivative of the function "y" shown below. 14) y = x2 + 8x + 3 x Solve the problem below. 15) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches from the east at 261 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 31 km away from the airport and the westbound plane is 18 km from the airport. FUNCTIONS, LIMITS and CONTINUITY. Find the intervals on which the function shown below is continuous. 16) y = x + 2 x2 - 8x + 7 5 A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number is given. Find a number > 0 such that for all x, 0 < x - c < f(x) - L < . 17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01 Find all points "x" where the function shown below is discontinuous. 18) Solve the "composite function ...

1. EVALUATING INTEGRALS.
Evaluate the integral shown below. (Hint: Try the substitution u
= (7x2 + 3).)
1)
x dx
(7x2 + 3)5
Evaluate the integral shown below. (Hint: Apply a property of
logarithms first.)
2)
ln x6
x
dx
1
Use the Fundamental Theorem of Calculus to find the derivative
shown below.
3)
d
dx
x5

2. 0
sin t dt
For the function shown below, sketch a graph of the function,
and then find the SMALLEST possible value and the
LARGEST possible value for a Riemann sum of the function on
the given interval as instructed.
4) f(x) = x2 ; between x = 3 and x = 7 with four rectangles of
equal width.
^
CHARACTERISTICS and BEHAVIOR OF FUNCTIONS.
Use l'Hopital's rule to find the limit below.
5) lim
x
5x + 9
6x2 + 3x - 9
^
Use l'Hopital's rule to find the limit below. (Hint: The
indeterminate form is f(x)g(x).)
6) lim
x
1 + 2
x3
x
2

3. Solve the following problem.
7) The 9 ft wall shown here stands 30 feet from the building.
Find the length of the shortest straight beam that will
reach to the side of the building from the ground outside the
wall.
9' wall
30'
Hint: Let "h" be the height on the building where the ladder
touches; let "x" be the distance on the ground
between the wall and the foot of the ladder. Use similar
triangles and the Pythagorean Theorem to write the
length of the beam "L" as a function of "x". Also note that a
radical function is minimized when it radicand is
minimized.
For the function shown below, identify its local and absolute
extreme values (if any), saying where they occur.
8) f(x) = -x3- 9x2 - 24x + 3
3
Find a value for "c" that satisfies the equation f(b) - f(a)
b - a
= f (c) in the conclusion of the Mean Value Theorem for the
function and interval shown below.

4. 9) f(x) = x +
75
x
, on the interval [3, 25]
DERIVATIVES.
Find the equation of the tangent line to the curve whose
function is shown below at the given point.
10) x5y5 = 32, tangent at (2, 1)
Use implicit differentiation to find dy/dx.
11) xy + x + y = x2y2
Given y = f(u) and u = g(x), find dy/dx = f (g(x))g (x).
12) y = u(u - 1), u = x2 + x
4
Find y .
13) y = (4x - 5)(4x3 - x2 + 1)
Find the derivative of the function "y" shown below.
14) y =
x2 + 8x + 3
x
Solve the problem below.
15) One airplane is approaching an airport from the north at 163
km/hr. A second airplane approaches from the east

5. at 261 km/hr. Find the rate at which the distance between the
planes changes when the southbound plane is 31
km away from the airport and the westbound plane is 18 km
from the airport.
FUNCTIONS, LIMITS and CONTINUITY.
Find the intervals on which the function shown below is
continuous.
16) y =
x + 2
x2 - 8x + 7
5
A function f(x), a point c, the limit of f(x) as x approaches c,
and a positive number is given. Find a number > 0 such
that for all x, 0 < x - c < f(x) - L < .
17) f(x) = 10x - 1, L = 29, c = 3, and = 0.01
Find all points "x" where the function shown below is
discontinuous.
18)
Solve the "composite function" problem shown below.
19) If f(x) = x + 4 and g(x) = 8x - 8, find f(g(x)). What is
f(g(0))?
Find the limit shown below, if it exists.

6. 20) lim
x 5
x2 - 25
x2 - 6x + 5
6
QUESTION 1
1. Choose the one alternative that best completes the statement
or answers the question. Solve the problem. Round dollar
amounts to the nearest dollar.
Find the yearly straight-line depreciation of a home theatre
system including the receiver, main audio speakers, surround
sound speakers, audio and video cables, and blue-ray player that
costs $3100 and has a salvage value of $900 after an expected
life of 5 years in a hotel lobby.
$900
$180
$440
$620
10 points
QUESTION 2
1. Solve the problem. Round unit depreciation to nearest cent
when making the schedule, and round final results to the nearest
cent.

7. A barge is expected to be operational for 280,000 miles. If the
boat costs $19,000.00 and has a projected salvage value of
$1900.00, find the unit depreciation.
$0.06
$0.60
$0.70
$0.07
10 points
QUESTION 3
1. Solve the problem. Round unit depreciation to nearest cent
when making the schedule, and round final results to the nearest
cent.
A construction company purchased a piece of equipment for
$1520. The expected life is 9000 hours, after which it will have
a salvage value of $380. Find the amount of depreciation for the
first year if the piece of equipment was used for 1800 hours.
Use the units-of-production method of depreciation.

8. $177.33
$136.50
$304.00
$228.00
10 points
QUESTION 4
1. Solve the problem using the information given in the table
and the weighted-average inventory method. Round to the
nearest cent.
Calculate the average unit cost.
Date of Purchase
Units Purchased
Cost Per Unit
Beginning Inventory
25
$32.12
March 1
70
$25.24
June 1
65
$36.24
August 1
40
$20.81
$32.90

9. $143.95
$28.79
$24.77
10 points
QUESTION 5
1. Solve the problem using the information given in the table
and the weighted-average inventory method. Round to the
nearest cent.
Calculate the cost of ending inventory.
Date of Purchase
Units Purchased
Cost Per Unit
Beginning Inventory
25
$33.18
March 1
70
$28.60
June 1
65
$38.75

10. August 1
40
$21.49
Units Sold
68
$1461.32
$3116.05
$4298.00
$4098.50
10 points
QUESTION 6
1. Solve the problem using the information given in the table

11. and the weighted-average inventory method. Round to the
nearest cent.
Calculate the cost of goods sold.
Date of Purchase
Units Purchased
Cost Per Unit
Beginning Inventory
25
$34.13
March 1
70
$27.34
June 1
65
$35.61
August 1
40
$20.77
Units Sold
62
$4079.63
$1832.87
$9992.13
$5912.50
10 points

12. QUESTION 7
1. Solve the problem. Use a fraction for the rate and round
dollar amounts to the nearest cent.
Jeremy James is depreciating solar panels purchased for $3600.
The scrap value is estimated to be $900. He will use double-
declining-balance and depreciate over 6 years. What is the first
year's depreciation?
$1200.00
$450.00
$600.00
$900.00
10 points
QUESTION 8
1. Solve the problem. Use a fraction for the rate and round
dollar amounts to the nearest cent.
Eric Johnson is depreciating a kitchen oven range purchased for
$1720. The scrap value is estimated to be $172. He will use
double-declining-balance and depreciate over 30 years. What is
the first year's depreciation?
$57.33

13. $103.20
$51.60
$114.67
QUESTION 9
1. Solve the problem. Use a fraction for the rate and round
dollar amounts to the nearest cent.
Jane Frankis is depreciating a train engine purchased for
$86,000. The scrap value is estimated to be $5000. She will use
double-declining-balance and depreciate over 40 years. What is
the first year's depreciation?
$2025.00
$4050.00
$4300.00

14. $2150.00
10 points
QUESTION 10
1. Find the depreciation for the indicated year using MACRS
cost-recovery rates for the properties placed in service at
midyear. Round dollar amounts to the nearest cent.
Property Class
Depreciation Year
Cost of Property
3-year
3
$86,600.00
$28,863.78
$17,320.00
$12,825.46
$16,627.20