1. A person breathes in and out every three seconds. The volume of air in
the persons lungs varies between a minimum of 2 liters and a maximum
of 4 liters. Express the volume of air in the persons lungs in the form
y = A sin t + C.
2. Spring-mass system
T
Worksheet 1 Solution
1. At a selling price of $17 per book, a publisher is willing to publish 5
million copies of a book while the demand is 5.7 million copies. When
the selling price is increased to $19, the supply and demand change to
6 million and 5.3
MATH 151: Applied Calculus I
Test 1
June 28, 2012
Please write clearly and put a box around your nal answer. Cross out any unwanted
material.
1. [10 points] The supply and demand curves for a product are given by q = 0.5p 25 and q =
165 0.5p, respectively
MATH 151: Applied Calculus I
Study Guide 3
The exam is 2 hours in-class. You are allowed to bring one sheet of notes
(8.5 11) and a graphing calculator. Cell phones, iPads, iPods, etc. cannot
be used as calculators. The exam is cumulative, but will be foc
Worksheet 3
Evaluate the followings with Wolfram Alpha. For problems 1-6, simply
the nal answers.
1. f (x), if f (x) = ex sin x
2. f (x), if f (x) = ln(xe7x )
3. f (x), if f (x) = e2x + e
4. f (x), if f (x) =
5. f (x), if f (x) =
cos x
1+x2
cos2 x + 1
6.
Worksheet 1
1. The sporting goods company FootLocker sells mens Jordan 3D Wristband at $5.99 each. John wants to order a certain quantity of wristbands online and re-sell them at a higher price in order to earn money.
(a) For priority mail via USPS, the t
MATH 151: Applied Calculus I
Final Exam - Session 1
Spring, 2013
Please write clearly and put a box around your nal answer. Cross out any unwanted
material.
1. [10 points] Find the rst derivatives of the following functions:
(a) f (x) = (x2 + x)/ x
(b) f
MATH 151: Applied Calculus I
Test 2 - Session 2
March 20, 2013
6. f (x) =
Please write clearly and put a box around
your nal answer. Cross out any unwanted
material.
3x2 + 5
1. f (x) = x3 3x2 + 5x
7. f (x) = x ln (2x 7)
2. f (x) = e3x
8. f (x) = ecos(x
2)
MATH 151: Applied Calculus I
Test 2 - Session 1
March 20, 2013
6. f (x) =
Please write clearly and put a box around
your nal answer. Cross out any unwanted
material.
3x2 + 5
1. f (x) = x3 3x2 + 5x
7. f (x) = x ln (2x 7)
2. f (x) = e3x
8. f (x) = ecos(x
2)
MATH 151: Applied Calculus I
Study Guide 1
The test is 1-hour in-class. You are allowed to bring one sheet of notes
(8.511). Cell phones, iPads, iPods, etc. CANNOT be used as calculators.
The test will cover the topics listed below.
1. Linear functions (1
Worksheet 1 Solution
1. The sporting goods company FootLocker sells mens Jordan 3D Wristband at $5.99 each. John wants to order a certain quantity of wristbands online and re-sell them at a higher price in order to earn money.
(a) For priority mail via US
MATH 151: Applied Calculus I
Study Guide 2
The test is 1-hour minutes in-class. You are allowed to bring one sheet of notes (8.5 11, front and back) and
a graphing calculator. Cell phones, iPads, iPods, etc. cannot be used as calculators. The test will co
MATH 151: Applied Calculus I
Final Exam
Summer, 2012
Please write clearly and put a box around your nal answer. Cross out any unwanted
material.
1. [10 points] Find the rst derivatives of the following functions:
2
(a) f (x) = x cos(ex )
(b) f (x) = (x4 /
MATH 151: Applied Calculus I
Test 2
July 12, 2012
Please write clearly and put a box around your nal answer. Cross out any unwanted
material.
1. [10 points] Find the rst derivatives of the following functions:
(a) f (x) = 3x2 + 5
(b) f (x) = ln (2x 7)
(c)
Worksheet 2: Exponential functions
The half-life of radioactive carbon-14 is about 5730 years.
1. What is the continuous decay rate of carbon-14?
2. In 1947, earthenware jars containing what are known as the Dead Sea
Scrolls were found by an Arab Bedouin
Worksheet 3 Solutions
Consider the function f (x) = x3 3x2 in the region 1 x 3.
1. Find the local maxima and local minima of f (x).
Solutions f (x) = 3x2 6x. Setting this to zero gives x = 0 or x = 2.
Using the rst derivative test, it is easy to verify th
Worksheet 3
Consider the function f (x) = x3 3x2 in the region 1 x 3.
1. Find the local maxima and local minima of f (x).
2. Find the global maxima and global minima of f (x).
3. Find the inection points of f (x).
4. Graph the function without using a gra
Worksheet 4 Solutions
1. The demand equation for a quantity q of a product at p dollars is
p = 4000 5q. Companies producing the product report the cost, C,
in dollars, to produce a quantity q is C = 6q + 5. What production
level earns the company the larg
MATH 151: Applied Calculus I
Test 1 - Session 1
February 20, 2013
Please write clearly and put a box around your nal answer. Cross out any unwanted
material.
1. [10 points] The supply and demand curves for a product are given by q = 0.5p 25 and q =
165 0.
MATH 151: Applied Calculus I
Final Exam - Session 2
Spring, 2013
Please write clearly and put a box around your nal answer. Cross out any unwanted
material.
1. [10 points] Find the rst derivatives of the following functions:
(a) f (x) = (x2 + x)/ x
(b) f
Worksheet 5 Solutions
1. The demand equation for a quantity q of a product at p dollars is
p = 4000 5q. Companies producing the product report the cost, C,
in dollars, to produce a quantity q is C = 6q + 5. What production
level earns the company the larg
Worksheet 6 Solutions
The total cost C, in thousands of dollars, of a certain production is given
by the short-run Cobb-Douglas cost curve
C(q) = 2q 3/2 + 1 ,
where 0 q 10 is the number of items in hundreds.
1. What is the xed cost of the production?
Solu
Worksheet 4 Solutions
Consider the function f (x) = 1/(x2 1) in the interval 1/2 x 1/2.
1. Find all local maxima and minima of f (x).
f (x) =
2x
= 0 2x = 0 x = 0
1)2
(x2
Using the rst or second derivative test, you can conrm that this is a
local maximum.
Worksheet 2: Exponential functions
1. The half-life of radioactive carbon-14 is about 5730 years. A fossil is
found that has 35% carbon-14 compared to the living sample. How old
is the fossil? Solve using the base e and base a exponential functions.
Solut
Worksheet 3 Solutions
1. The Bay of Fundy in Canada has the largest tides in the world. The
dierence between low and high water levels is 15 meters (nearly 50
feet). At a particular point the depth of the water, y meters, is given
as a function of time, t
Consider the cost function C(q) = 0.3q 3 0.8q 2 + 4q + 8 and revenue
function R(q) = 6q 2q 2 .
1. Sketch the graph of y = f (x).
2. Estimate f (1) by using a point at x = 1 and a point at x = 1.2.
3. Estimate f (1) by using a point at x = 1 and a point at
Find the rst and second derivatives of the following functions.
1. y = 5x3 + 7x2 3x + 1
2. y = 6x2 + 3x3 4x1/2
3. y = 8 ln(2x + 1)
4. y =
e2x
x2 +1
5. y =
x2 +3x+2
x+1
6. y =
x2 +2
3
2
7. y = ln(sin x + cos x)
8. y =
x3
9 (3 ln x
9. y =
x2 + x+1
x3/2
1)
Keplers third law of planetary motion states that P 2 = kd3 , where P
represents the time, in earth days, it takes a planet to orbit the sun once, d
is the planets average distance, in miles, from the sun, and k is a constant.
1. If k = 1.65864 1019 , wri
1. Locate the local maxima, local minima, and the points of inection of
2
the Gaussian function f (x) = ex . Sketch the graph of this function.
4
2. Now consider the super Gaussian function f (x) = ex . Locate the
local maxima, local minima, and the point