Math 1260 Exam 3 Solutions Spring 2009
1.) 195 + 180 0.171 2073 2.) f (2) = P4 (2) = 0
3.) Immediately after the injection on the rst day, the patients body contains A mg of the drug. Immediately after the injection on the second day, the amount of the dr
Name
Date
Math 10260 Exam 1 Review Activity
dy
= e0.5t + 3t2 , y (0) = 1.
dt
Q 2: Evaluate the following integrals without your calculator:
Q 1: Solve the initial value problem
xe3x dx
a.
b.
2
(x 1)25 dx
d.
e.
0
(Ans: y = 2e0.5t + t3 + 3)
3
(ln x)2
dx
x
x
Part I: Multiple Choice Questions (5 Points Each)
1. Find the distance between the two points (1, 2, 3) and (3, 1, 6).
(a)
14
(b) 14
(c) 6
(d) 4
(e)
17
2. Suppose that f (x, y ) is a function such that
f (3, 4) = 10
f
(3, 4) = 1
x
f
(3, 4) = 3
y
The equat
Math 10260 Exam 2 Solutions - Spring 2006
1. Find the distance between the two points (1, 2, 3) and (3, 1, 6).
(1 3)2 + (2 1)2 + (3 6)2 = 14
2. Suppose that f (x, y ) is a function such that
f
(3, 4) = 1
x
f (3, 4) = 10
f
(3, 4) = 3
y
The equation of the
Department of Mathematics
University of Notre Dame
Math 10260 Bus. Calc. II
Spring 2009
Name:
Instructor:
Exam II
March 5, 2009
This exam is in 2 parts on 11 pages and contains 15 problems worth a total of 100 points. You
have 1 hour and 15 minutes to wor
SOLUTIONS TO EXAM 2 MATH 10260, SPRING 2009
1. (z 3) = 2(x 1) + 5(y + 2) = 2x + 5y + 11.
2.
(2 1)2 + (1 1)2 + (1 2)2 = 2.
3. We have
f
f
= y ex ,
= x.
x
y
f
f
= 0 x = 0,
= 0 y = ex = 1.
y
x
Hence (0, 1) is the only critical point of the function.
4. The x
Name
Date
Math 10260 Exam 2 Review Activity
1. Do the points (1, 2, 0), (5, 6, 1) and (9, 3, 2) form a right triangle?
Ans. No
2. Let f (x, y ) = x2 + y 2 .
Draw level curves of f (x, y )
Draw the graph of x-section of f (x, y ) where x = 1.
Draw the g
Part I: Multiple Choice Questions (5 Points Each)
1. The size of a population of certain species of animals in thousands is modeled by
the dierential equation
dp
= g (p)
dt
where the graph of g (p) is displayed in Figure 1.
Which of the following statemen
Math 10260 Exam 3 Solutions - Spring 2006
dp
= g (p) < 0 on the interval
dt
dp
0 < p < 2 and p > 10, p(t) is decreasing there. On the other hand,
= g (p) > 0 for
dt
2 < p < 10, p(t) is increasing there. Therefore, if the initial population p(0) is 3 thous
Department of Mathematics
University of Notre Dame
Math 10260 Bus. Calc. II
Spring 2009
Name:
Instructor:
Exam III
April 16, 2009
This exam is in 2 parts on 11 pages and contains 15 problems worth a total of 100 points. You
have 1 hour and 15 minutes to w
Math 1260 Exam 3 Solutions Spring 2009
195 + 180
0.171
2073
2.) f (2) = P4 (2) = 0
1.)
3.) Immediately after the injection on the rst day, the patients body contains A mg of the drug.
Immediately after the injection on the second day, the amount of the d
Math 10260 Exam 3 Review Activity
dy
= g (y ) where the graph of
dt
g (y ) is given in Figure 1. (a) Find the equilibrium solutions and
determine their stability. (b) Use graphical method to sketch
the graph of the solution for the given initial value; yo
Name:
Math. 10260, Final Exam
May 6, 2009
Instructor:
Be sure that you have all 16 pages of the test.
Calculators are allowed for this examination.
The exam lasts for two hours.
The Honor Code is in eect for this examination, including keeping your answer
Name
Date
Math 10260 Final Exam Review Activity
1. The demand function D and supply function S of a model of jeans for the clothing company Lucky
Clovers Wear are given, in term of quantity q , by
p = e42q ;
p = eq+1
(p 0)
(a) Give a sketch of the demand
Math 1260 Exam 1 Solutions Spring 2009
1.) Taking the integral of both sides of the equation Q (x) = 200x1/2 we nd that Q(x) =
200x1/2 dx = 400x1/2 + c. We can nd c by pluging Q = 500 and x = 4 into the above equation:
500 = 800 + c or c = 300. Therefore
Department of Mathematics
University of Notre Dame
Math 10260 Bus. Calc. II
Spring 2009
Name:
Instructor:
Exam I
February 5, 2009
This exam is in 2 parts on 11 pages and contains 15 problems worth a total of 100 points. You
have 1 hour and 15 minutes to w
Department of Mathematics University of Notre Dame Math 10260 Bus. Calc. II Spring 2009
Name: Instructor:
Exam III
April 16, 2009 This exam is in 2 parts on 11 pages and contains 15 problems worth a total of 100 points. You have 1 hour and 15 minutes to w
Math 10260 Final Exam Solutions - Spring 2009
1. Since f (x) is a probability density function we have 2. P (3 < X < 4) = 0.2 3. The producer surplus (PS) is equal to the area of the rectangle [0, 8] [0, 5] minus the area 8 under the supply curve. That is
Name: Math. 10260, Final Exam May 6, 2009 Instructor:
Be sure that you have all 16 pages of the test. Calculators are allowed for this examination. The exam lasts for two hours. The Honor Code is in eect for this examination, including keeping your answer
University of Notre Dame
Skip to content. | Skip to navigation
Personal tools
Log in
Search Site
only in current section
Advanced Search
Sections
Home
Courses
About OCW
Help
Feedback
Search
You are here: Home Mathematics Calculus II for Business
Calculus
University of Notre Dame
Skip to content. | Skip to navigation
Personal tools
Log in
Search Site
only in current section
Advanced Search
Sections
Home
Courses
About OCW
Help
Feedback
Search
You are here: Home Mathematics Calculus II for Business
Calculus
Math 10260 Projects Fall 2009
The goal of these projects is to give you the opportunity to make your own connections between mathematics and modern society by considering a wide variety of problems ranging from economic and environmental issues to social
Math 1260 Exam 1 Solutions Spring 2009
1.) Taking the integral of both sides of the equation Q (x) = 200x1/2 we nd that Q(x) = 200x1/2 dx = 400x1/2 + c. We can nd c by pluging Q = 500 and x = 4 into the above equation: 500 = 800 + c or c = 300. Therefore
Department of Mathematics University of Notre Dame Math 10260 Bus. Calc. II Spring 2009
Name: Instructor:
Exam I
February 5, 2009 This exam is in 2 parts on 11 pages and contains 15 problems worth a total of 100 points. You have 1 hour and 15 minutes to w
SOLUTIONS TO EXAM 2 MATH 10260, SPRING 2009 1. (z 3) = 2(x 1) + 5(y + 2) = 2x + 5y + 11. 2. (2 1)2 + (1 1)2 + (1 2)2 = 2. 3. We have f f = y ex , = x. x y f f = 0 x = 0, = 0 y = ex = 1. y x Hence (0, 1) is the only critical point of the function. 4. The x
Department of Mathematics University of Notre Dame Math 10260 Bus. Calc. II Spring 2009
Name: Instructor:
Exam II
March 5, 2009 This exam is in 2 parts on 11 pages and contains 15 problems worth a total of 100 points. You have 1 hour and 15 minutes to wor
Part I: Multiple Choice Questions (5 Points Each)
Consumption in billions of
barrels per year
1. The graph below displays the rate at which oil was consumed by the U.S. from
1980 to 2000. Use the midpoint rule with t = 10 to estimate the total amount
of o
Math 10260 Exam 1 - Solutions - Spring 2006
1. Let us set 1980 to stand for t = 0. The total amount of oil consumed during 1980 to 2000 =
The area under the graph
[r(5) + r(15)] t = (6 + 8) 10 = 140.
1
2. Using integration by substitution u = ln x. Then