MATH 31B: SELECTED HW SOLUTIONS AND QUESTIONS FROM REVIEW SESSION
JOHN SUSICE
Section 8.1
Throughout this section we will obey the LIPET rule to choose our u. This means that our order of preference
for u-substituion is given in descending order by:
(1)
(
Math 31B/4
Fall 2013
Exam 1
October 21, 2013
70 points
Name (Print):
This exam consists of 8 pages (including this cover
page) and 4 problems. Please check to see if any pages
are missing.
Rules. No calculators, computers, notes, books,
or other aids are
Exam Review 1
Brian Van Koten
November 22, 2013
Problem 1 is related to Problem 1(b) from the second midterm and Problem 42 in Section 11.1. It will come up when we discuss the Taylor series of
f (x) = ex .
Problem 1. Let x be a constant. Show that limn
x
Jon Paprocki
1
Problem solutions
(1) Evaluate
Z
e x
dx
x
(2) Let m, n be positive nonzero integers. Compute the possible values of
cos(mx)
x/2 cos(nx)
lim
(3) Evaluate the integral
Z
tan1 (x) dx
(4) Let n be a nonzero integer. Find the domain on which th
HW 10
LAST NAME:
Due: Mar 6, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: This HW practices arc-length and surface-area calculations, and limits of sequences. Sections 9.1, 11.1-11.2.
Problem 1: Compute the length of the curve y = a log
for 0 x
a/ ,
2
wh
HW 11
LAST NAME:
Due: Mar 8, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: This HW practices limits of sequences and infinite series. Sections 11.1-11.4.
Problem 1: Define cfw_ xn nN such that for L =
1
2+
1
1+ 2+1.
we have limn = L. Prove the limit by fin
HW 7
LAST NAME:
Due: Feb 10, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: This HW practices techniques of integration as well as trig and hyperbolic substitutions. Do problems in Sections 8.2-8.4 first!
Z q
Z
2
2
1x 1+x
dx
1 x4
Problem 1: Compute
ANSWER
HW 2
LAST NAME:
Due: Jan 20, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: Practice trig functions, higher derivatives, implicit differentiation, related rates, lHopitals rule in Sections 1.4, 2.6, 3.5, 3.8, 3.9, 7.7.
Problem 1: Find the equation of the ta
HW 12
LAST NAME:
Due: Mar 17, 2017
FIRST NAME:
SECTION:
SCORE:
ID #:
Note: This HW practices alternating series, ratio/root tests, power and Taylor series. Sections 11.4-11.7.
Problem 1:
Decide whether the series converge absolutely, conditionally or not
HW 5
LAST NAME:
Due: Feb 1, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: This HW reemphasizes concepts/problems from the first midterm and practices exponentials, logs and inverse functions
Problem 1: Express the rational number 2/7 (written in
base-10) a
HW 13
LAST NAME:
Due: Mar 19, 2017 (final)
FIRST NAME:
SECTION:
Note: This HW gives you additional practice of all material covered.
Z xx
Problem 1: Compute f 0 ( x ) for f ( x ) =
0
tt dt.
Problem 3: Compute lim
x 0
ANSWER
1
x
1
ex 1
ANSWER
Problem 2: F
HW 9
LAST NAME:
Due: Feb 27, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: This HW practices Taylors Theorem and Arc-Length. Read, and try the exercises in, Sections 9.1 and 9.4 to get some ideas first!
Problem 1: Find the n-th order Taylor polynomial Tn (
HW 6
LAST NAME:
Due: Feb 6, 2017
FIRST NAME:
SECTION:
SCORE:
ID #:
Note: This HW practices computations of singular limits, substitution rule and integration by parts. Sections 5.7, 7.7, 8.1
Problem 1: Compute lim
sin( x ) 1/x2
x 0
x
ANSWER
(1 + x )1/x
HW 8
LAST NAME:
Due: Feb 15, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: This HW practices trig integrals and partial fractions. Try the exercises in Sections 8.2 and 8.5 to get some easier problems first!
Z
Z
Problem 1: Compute
0
sin( x )2 cos( x )4 dx
HW 1
LAST NAME:
Due: Jan 18, 2017
FIRST NAME:
SECTION:
ID #:
SCORE:
Note: As a warm-up, practice problems in Sections 1.1-1.4, 3.1-3.7 from the textbook.
Problem 3:
Find the smallest integer larger than 10100
that is divisible by 7. Hint: Follow the remai
Course Syllabus
Math 31B - Integration and Infinite Series
Lectures 3 & 4 | Winter 2016
Course information
This is the second quarter of a standard course in calculus. In this course we will cover transcendental functions, methods and applications of inte
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Why is it called negative skew? Because the long "tail"
is on the negative side of the peak.
People sometim
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DERIVATIVES OF
INVERSE TRIGONOMETRIC
FUNCTIONS
The derivative of y = arcsin x
The derivative of y = arccos x
The derivative of y = arctan x
The derivative of y = arccot x
The derivative of y = a
Math 31B-2: Homework Week 3
1. Monday was a holiday.
2. Wednesdays Lecture: Do 8.1.6, 8.1.8, 8.1.16, 8.1.37, 8.1.43, 8.1.47, 8.2.5, and 8.2.9 in
Rogawski.
3. Fridays Lecture: Do 8.2.32, 8.2.33, 8.2.51, 8.3.15, 8.3.23, 8.3.28, and 8.3.38 in Rogawski.
Math 31B-2: Homework Week 1
1. Do problems 7.1.1, 7.1.16, 7.1.19, 7.1.25, 7.1.31, 7.1.74, 7.1.81, 7.1.82 in Rogawski. [If you
find yourself confused about exponentials, do a few more of the early problems in this
section as a reminder.]
2. Do problems 7.2
Math 31B-2: Homework Week 5
1. Mondays Lecture: Do 8.8.7, 8.8.9, 8.8.25, 8.8.31, 8.8.34, and 8.8.41 in Rogawski.
2. Wednesdays Lecture: Do 8.8.13, 8.8.16, 8.8.26, 8.8.28, 8.8.42, 8.8.43, and 8.8.47 in Rogawski.
3. Fridays Lecture: Do 9.1.9, 9.1.10, 9.1.14
Math 31B-2: Homework Week 6
1. Mondays Lecture: Do 9.2.1, 9.2.2, 9.2.4, 9.2.5, 9.2.9, and 9.2.13 in Rogawski.
2. Wednesdays Lecture: Do 9.4.1, 9.4.3, 9.4.9, 9.4.22, 9.4.28, 9.4.51, 9.4.52, and 9.4.55 in
Rogawski.
3. Fridays Lecture: Do 9.4.33, 9.4.35, 9.4