Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 3
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, February 7, 2002
Section 5.7:
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21-112 Calculus II:
Homework #7 Solutions
Kevin C. Lee
November 18, 2004
1
7.1
Problem 8:
C(x, y, z) = 3xy + 10yz + 5xz. The reason for 10yz is that there are two yz sides.
Problem 18:
To nd out the level curve, one needs to solve rst the height of the le
21-112 Calculus II:
Homework #9 Solutions
Chris Mirabito
December 7, 2004
1
7.4 #4 Minimize 2 x2 3xy + y 2 +
1
2
subject to the constraint 3x y 1 = 0.
A: Use the method of Lagrange Multipliers. In this case we have
1 2
1
x 3xy + y 2 +
2
2
g(x, y) = 3x y 1
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21-112 Calculus II:
Homework #8 Solutions
Kevin C. Lee
December 2, 2004
Section 7.3
Problem 2:
f (x, y) = 1/2x2 + y 2 3x + 2y 5. Take the partial derivatives with respect to x and y
and equate them to 0. We have:
f
=x3=0
x
x=3
f
= 2y + 2 = 0
y
y = 1
Hence
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21-112 Calculus II:
Homework #2 Solutions
Kevin C. Lee
September 15, 2004
1
6.3
Problem 38:
It is the total amount of pollutants in tons that are discharged from 1995 to 1997.
Problem 42:
(a) The total prot is simply the integral of the marginal prot func
21-112 Calculus II:
Homework #4 Solutions
Chris Mirabito
October 7, 2004
6.6 #18 Determine
e x
x
dx by making an appropriate substitution.
1
1
A: In this case the appropriate subsitution to make is u = x = x 2 . Then du = 1 x 2 dx.
2
The issue here is tha
21-112 Calculus II:
Homework #3 Solutions
Kevin C. Lee
September 24, 2004
1
6.5
Problem 10:
The formula to calculate amount with the interest compounded continuously is P ert (ref.
to page 280). Hence the average value of the money during the next 20 year
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Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Announcement of Test #4
Test #4 will be administered in lecture on Friday, May 3, 2002. This is a
closed-book and closed-note exam. Calculators are not permitted
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Announcement of Test #2
Test #2 will be administered in lecture on Friday, March 1, 2002. This is a
closed-book and closed-note exam. Calculators are not permitt
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Announcement of Test #1
Test #1 will be administered in lecture on Friday, February 8, 2002.
This is a closed-book and closed-note exam. Calculators are not
perm
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 6
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, February 28, 2002
Section 9.1:
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 2
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, January 31, 2002
Section 5.4:
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 4
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, February 14, 2002
Section 6.2:
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 7
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, March 12, 2002
Section 7.2: Pr
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 1
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, January 24, 2002
Section 5.1:
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 5
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, February 21, 2002
Section 6.3:
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 10
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, March 28, 2002
Section 8.1: P
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 8
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, March 14, 2002
Section 7.4: Pr
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 9
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, March 21, 2002
Section 7.5: Pr
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Assignment 11
Solutions to all the following problems should be written up and
handed in to your TA.
Due in recitation on Thursday, April 11, 2002
Section 8.2: P
Department of Mathematical Sciences
Carnegie Mellon University
Spring 2002
21-112 Calculus II
Announcement of Test #3
Test #3 will be administered in lecture on Friday, March 22, 2002. This is
a closed-book and closed-note exam. Calculators are not permit
21-112 Calculus II:
Homework #1 Solutions
Kevin C. Lee
September 10, 2004
1
6.1
Problem 46:
(a)
s(t) =
(32t) dt = 16t2 + C
Since we know at t = 0, s(t) = 400, substitute t = 0 into s(t), we get:
s(0) = C = 400
Therefore,
s(t) = 16t2 + 400
(b)
The rock rea