Math 132 - Spring, 2009 Homework 2 - Due Jan 23 Name: _Solutions_
Mathematics Quote: It is true that Fourier had the opinion that the principal aim of mathematics was
public utility and explanation of natural phenomena; but a philosopher like him should h
Math 132 - Spring, 2009
Quiz 2
Name: _Solutions_
No Calculator. Show your work in detail.
1. (4pts) Evaluate the definite integral. You may leave any irrational number (e, a , lnb, sinc, . . . ) in
ub
your answer. If the substitution method is used, state
Math 132 - Spring, 2009
Quiz 3
Name: _Solutions_
No Calculator. Show your work in detail.
1. (10pts) Find the general antiderivatives. If the substitution method is used, state first u, du and
fudu. Evaluate the definite integrals. If the substitution me
Math 132 - Spring, 2009
Quiz 4
Name: _Solutions_
No Calculator. Show your work in detail.
1. (10pts) Find the general antiderivative or evaluate a definite integral.
ux, dudx
a. (a) x sinxdx
dvsinxdx, v sinxdx
1
1
x cosx
x3
1 3
x
9
ulnx, du 1 dx
x
v
1
Math 132 - Spring, 2009
Quiz 6
Name: _Solutions_
No Calculator. Show your work in detail.
1. (10pts) Find the general antiderivative or evaluate a definite integral.
sin 2 cos 2 1, sec 2 tan 2 1, sin 2 1 1 cos2, cos 2 1 1 cos2
2
2
usinx
a. (a) sin 6 x cos
Math 132 - Spring, 2009
Quiz 5
Name: _Solutions_
No Calculator. Show your work in detail.
1. (10pts) Find the general antiderivative or evaluate a definite integral.
ue 2x , du2e 2x dx
a. (a) e 2x sinxdx
e 2x cosx cosx2e 2x dx
dvcosxdx, v sinxdxcosx
ue 2x
Math 132 - Spring, 2009
Quiz 8
Name: _Solutions_
Show your work in detail.
1. (2pts)
Version (a) Find the volume of the solid with cross-sectional area Ax 3e 2x for 0 x 1.
1
V 3e 2x dx 3 e 2x | 1 3 e 2 1 3 1 12
0
2
2
2
e
0
Version (b) Find the volume of t
Math 132 - Spring, 2009
Quiz 7
Name: _Solutions_
Show your work in detail.
1. (10pts) Sketch and find the area of the region bounded by the given curves.
a. Version (a) y 3x 2 and y 4 x 2
(1) Sketch both curves. Label scales of each axis. (2) Find interse
Math 132 - Spring, 2009
Quiz 9
Name: _Solutions_
Show your work in detail.
1. (10pts) The region H given below is bounded by the curve y x 2 , x 1 and the x-axis. Find the volume
of the solid obtained by revolving the region H about the given line. For ea
Math 132 - Spring, 2009
Quiz 10(a)
Name: Solutions_
Show your work in detail.
1. (5pts) The region H given below is bounded by the curve y x 2 , x 2 and the x-axis. Using the
Cylindrical Shell Method, find the volume of the solid obtained by revolving the
Math 132 - Spring, 2009
Hour Exam 1
Name: _Solutions_
No Calculator. Show your work in detail.
Identities: sin 2 cos 2 1, sec 2 tan 2 1, sin 2 1 1 cos2, cos 2 1 1 cos2
2
2
1. (71pts) Find the general antiderivatives.
u2e x , due x dx
ex
1 du 2u 1/2 C 2 e
Math 132 - Spring, 2009
Hour Exam 2
Name: _
Please follow instructions given for each problem and show your work in detail.
1. (10pts) Let R be the region bounded by curves y x 2 and y 4 x 2 .
(1) Sketch R at the right. Label scales of axes.
y
(2) Find in
Math 132 - Spring, 2009
Quiz 12
Name: _Solutions_
1. (4pts) For each sequence a n , (1) compute a 1 and a 2 ; (2) compute lim n a n without using calculator; and
(3) determine if the sequence a n is convergent or divergent. Provide your reason in detail t
Math 132 - Spring, 2009
Quiz 13
Name: _Solutions_
1. (8pts) For each of the following series, (1) give its name (if there is one);
(2) determine whether it converges or diverges and show your work and name the test you use.
a. Version (a) 1 k 1 it is an a
Math 132 - Spring, 2009
Quiz 14
Name: _Solutions_
1. (1pt) Version (a) Give a convergent geometric series. Version (b) Give a convergent p series.
k
(b) k0 12
(a) k0 1
2
k
2. (1pt) Version (a) Give a divergent p-series. Version (b) Give a convergent alte
Math 132 - Spring, 2009
Quiz 15
Name: _Solutions_
1. (1pt) Give an alternating p-series which converges only conditionally.
1 1 alternating harmonic series converges conditionally because
k
k1
converges.
k
k1
1 diverges and 1 k 1
k
k
k1
2. (1pt) Give a di
Math 132 - Spring, 2009
Quiz 11
Name: _Solutions_
Without using a calculator. Show your work in detail.
1. (2pts) Find the limit. Specify first the type of the limit.
2
Version (a) lim x x 2 e x lim x x x lim x 2x lim x 2x 0
x
e
e
e
1
1
lnx
lim x 1 x1/
Math 132 - Spring, 2009
Quiz 1
Name: _Solutions_
No Calculator. Show your work in detail.
1. Find the general antiderivative.
a. (4pts)
(a) x 2009 12
x
3 x 5e 2x 1. 1 x dx
x
x
x 2009 x 2 x 1/3 3 x 5e 2x 1. 1 x dx
x
1 x 2010 x 1 3 x 2/3 3 ln|x| 1 x 1 x
Math 132 - Spring, 2009 Homework 15 - Due March 17 Name: _Solutions_
Mathematics Quote: If others would but reflect on mathematical truths as deeply and as continuously as I
have, they would make my discoveries. - Gauss, Karl Friedrich (1777-1855), In J.
Math 132 - Spring, 2009 Homework 3 - Due Jan 27 Name: _Solutions_
Mathematics Quote: The so-called Pythagoreans, who were the first to take up mathematics, not only
advanced this subject, but saturated with it, they fancied that the principles of mathemat
Math 132 - Spring, 2009 Homework 5 - Due Feb 3 Name: _Solutions_
Mathematics Quote: The so-called Pythagoreans, who were the first to take up mathematics, not only
advanced this subject, but saturated with it, they fancied that the principles of mathemati
Math 132 - Spring, 2009 Homework 1 - Due Jan 21 Name: _Solutions for *_
Mathematics Quote: The greatest reward lies in making the discovery; recognition can add little or
nothing to that. - Neumann, Franz Ernst (1798 - 1895)
Notes: The purpose of this ass
Math 132 - Spring, 2009 Homework 4 - Due Jan 30 Name: _
Mathematics Quote: The mathematical sciences particularly exhibit order, symmetry, and limitation; and
these are the greatest forms of the beautiful. - Aristotle (ca 330 BC)
1. Reading Assignment:
Pa
Math 132 - Spring, 2009 Homework 10 - Due Feb 24 Name: _
Mathematics Quote: The effort of the economist is to "see," to picture the interplay of economic elements.
The more clearly cut these elements appear in his vision, the better; the more elements he
Math 132 - Spring, 2009 Homework 9 - Due Feb 20 Name: _
Mathematics Quote: To explain all nature is too difficult a task for any one man or even for any one age.
Tis much better to do a little with certainty, and leave the rest for others hat come after y
Math 132 - Spring, 2009 Homework 7 - Due Feb 13 Name: _Solutions_
Mathematics Quote: We used to think that if we knew one, we knew two, because one and one are two. We
are finding that we must learn a great deal more about and. - Sir Arthur Eddington (188
Math 132 - Spring, 2009 Homework 8 - Due Feb 17 Name: _Solutions_
Mathematics Quote: Be prepared. Luck is truly where preparation meets opportunity - Dr. Randy Pausch
- Last Lecture
1. Reading Assignment:
Page 441-453
2. Page 454: - turn in the problems w
Math 132 - Spring, 2009 Homework 6 - Due Feb 10 Name: _Solutions_
Mathematics Quote: The modern, and to my mind true, theory is that mathematics is the abstract form of
the natural sciences; and that it is valuable as a training of the reasoning powers no
Math 132 - Spring, 2009 Homework 18 - Due April 7 Name: _Solutions_
Mathematics Quote: "Mathematics is the science of what is clear by itself." In J. R. Newman (ed.) The
World of Mathematics, New York: Simon and Schuster, 1956.
1. Reading: Page 656-661 an
Math 132 - Spring, 2009 Homework 20 - Due April 14 Name: _Solutions_
Mathematics Quote: For a physicist mathematics is not just a tool by means of which phenomena can be
calculated, it is the main source of concepts and principles by means of which new th