Rice University
Department of Mathematics
Solutions
Math 101 - Fall 2009
Midterm Exam II
Problem 1. Evaluate the following limits:
(a) (5 points)
ex 1
ex
= lim 2 = +
x0
x0 3x
x3
lim
(LHospitals Rule was applied once for the
0
0
case.)
(b) (5 points)
lim+
Math 101 Fall 2000 Final Exam Solutions
Instructor: Richard Stong
Wednesday, December 13, 2000
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do all your
work
Math 101 Fall 2004 Final Exam
Instructors: Jennifer Wightman/Richard Stong
Wednesday, December 8, 2004
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do all yo
Math 101 Fall 2002 Final Exam
Instructors: Richard Evans/Richard Stong
Friday, December 13, 2002
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do all your
wor
Math 101 Fall 2001 Final Exam
Instructor: Richard Stong
Thursday, December 13, 2001
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do all your
work on the pape
Math 101 Fall 2000 Final Exam
Instructor: Richard Stong
Wednesday, December 13, 2000
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do all your
work on the pap
Problems for nal exam
- Problems from past common exam
2013 Fall Exam I (version A): 2, 10, 11, 12, 15, 17, 20, 22
2013 Fall Exam I (version B): 6, 8, 9, 10, 15, 17, 20, 22
2013 Fall Exam II (version A): 2, 3, 6, 8, 10, 13, 17, 18, 19, 21
2013 Fall Exam I
Fall 2014 Math 151
Exam 2B: Solutions
c 2014 Art Belmonte
Fri, 31/Oct
1. (b) Two limit denitions of f (a) are lim
xa
f (x) f (a)
xa
f (a + h) f (a)
. For f (x) = (2x + 1)3/2 and
h0
h
a = 1 , these are represented by choices (iii) and (ii),
respectively. T
Review for the nal
The total score is 250 (25% out of 100%). 10 work out problems will be given, where 5
problems are from Exam I, II, and III. The other 5 problems are listed below.
Part I: Common Exams
1. ( 17 of Exam I) lim
x
x2 6x 1 x
2. ( 21 of Exam
Fall 2014 Math 151
Exam 1A: Solutions
c 2014 Art Belmonte
Fri, 03/Oct
9. (d) We have
3t 2
lim
t 4t 2 + t + 1
=
=
See your exam for problem statements. Here are various
vector notations: v = v1 i + v2 j = v1 , v2 = [v1 , v2 ]. The
magnitude of v is denote
Math 101: Calculus I
Problem Set 7b
Due 11:59pm on Tuesday March 8
From the course syllabus: You should work individually on the problems at
first. Collaboration and discussion with others is encouraged, but only after you
have given the problems a good a
Math 101 Fall 2001 Final Exam Solutions
Instructor: Richard Stong
Thursday, December 13, 2001
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do all your
work o
Math 101 Fall 2002 Final Exam Solutions
Instructors: Richard Evans/Richard Stong
Friday, December 13, 2002
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please do al
Math 101 Fall 2004 Final Exam Solutions
Instructors: Jennifer Wightman/Richard Stong
Wednesday, December 8, 2004
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have three hours. Do all 12 problems. Please
Math 101 Spring 2008 Practice Test 1 Solutions
1) Find the derivative with respect to x.
Note: For problems like this, you dont necessarily have to simplify as much as
I did.
2
a) y = xx
= xx
y
ln y
=
2
ln xx
2
1 dy
y dx
= x2 ln x
1
= (x2 )( ) + 2x ln x
x
Math 101 Section 003 Midterm 1 Extra Extra Problem Solutions
Below are the solutions to the extra extra problems provided. Graphs have been omitted. Please see me
if you have trouble with graphs.
1. Let f (x) = x2 2x + 3.
(a) Notice that f (x) = x2 2x + 3
Math 101, Spring 2008, Exam 1
The exam consists of seven questions. You must show all your work to receive
full credit. Please indicate your nal answer clearly. Write the honor pledge on
your exam when nished. Good luck!
1) Find the derivative with respec
Math 101 Fall 2006 Exam 1
Instructor: S. Cautis/M. Simpson/R. Stong
Thursday, October 5, 2006
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have one hour and fteen minutes. Do all 7 problems.
Please do a
Math 101 Fall 2004 Exam 1
Instructor: Jennifer Wightman/Richard Stong
Thursday, September 30, 2004
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have one hour and fteen minutes. Do all 8 problems.
Please
Math 101 Fall 2002 Exam 1
Instructor: Richard Evans/Richard Stong
Tuesday, October 1, 2002
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have one hour and fteen minutes. Do all 7 problems.
Please do all
Math 101 Fall 2001 Exam 1
Instructor: Richard Stong
Tuesday, September 25, 2001
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have one hour and fteen minutes. Do all 7 problems.
Please do all your work o
Math 101 Fall 2000 Exam 1
Instructor: Richard Stong
Tuesday, October 3, 2000
Instructions : This is a closed book, closed notes exam. Use of calculators is
not permitted. You have one hour and fteen minutes. Do all 8 problems.
Please do all your work on t
Math 101: Calculus I
Problem Set 6b
Due 11:59pm, Tuesday February 23
From the course syllabus: You should work individually on the problems at
first. Collaboration and discussion with others is encouraged, but only after you
have given the problems a good
Math 101: Calculus I
Problem Set 11b
Due 11:59pm, Tuesday April 5
From the course syllabus: You should work individually on the problems at
first. Collaboration and discussion with others is encouraged, but only after you
have given the problems a good am
Math 101: Calculus I
Problem Set 10b
Due 11:59pm Tuesday March 29
From the course syllabus: You should work individually on the problems at
first. Collaboration and discussion with others is encouraged, but only after you
have given the problems a good am
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SECTION 5.3 The Fundamental Theorem of Calculus 399
This version says that if we take a function F, ﬁrst differentiate it, and then integrate the
result, we arrive back at the original function F, but in the form F (I7) — F(a). Taken
together, the two par
356 CHAPTER 4 Applications of Differentiation
2x2+5
22. f(x) = x2 +1
23—24 Find the antiderivative F of f that satisﬁes the given
condition. Check your answer by comparing the graphs of
fand F.
23. f(x) = 5x4 — 2x5, F(0) = 4
24. f(x) = 4 — 3(1 + x2)", F