MATH 31B: SELECTED HW SOLUTIONS AND QUESTIONS FROM REVIEW SESSION
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:
October 21, 2013
This exam consists of 8 pages (including this cover
page) and 4 problems. Please check to see if any pages
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
(2) Let m, n be positive nonzero integers. Compute the possible values of
(3) Evaluate the integral
tan1 (x) dx
(4) Let n be a nonzero integer. Find the domain on which th
Due: Mar 6, 2017
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
Due: Mar 8, 2017
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 =
we have limn = L. Prove the limit by fin
Due: Feb 10, 2017
Note: This HW practices techniques of integration as well as trig and hyperbolic substitutions. Do problems in Sections 8.2-8.4 first!
Problem 1: Compute
Due: Jan 20, 2017
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
Due: Mar 17, 2017
Note: This HW practices alternating series, ratio/root tests, power and Taylor series. Sections 11.4-11.7.
Decide whether the series converge absolutely, conditionally or not
Due: Feb 1, 2017
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
Due: Mar 19, 2017 (final)
Note: This HW gives you additional practice of all material covered.
Problem 1: Compute f 0 ( x ) for f ( x ) =
Problem 3: Compute lim
Problem 2: F
Due: Feb 27, 2017
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 (
Due: Feb 6, 2017
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
(1 + x )1/x
Due: Feb 15, 2017
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!
Problem 1: Compute
sin( x )2 cos( x )4 dx
Due: Jan 18, 2017
Note: As a warm-up, practice problems in Sections 1.1-1.4, 3.1-3.7 from the textbook.
Find the smallest integer larger than 10100
that is divisible by 7. Hint: Follow the remai
Math 31B - Integration and Infinite Series
Lectures 3 & 4 | Winter 2016
This is the second quarter of a standard course in calculus. In this course we will cover transcendental functions, methods and applications of inte
Data can be "skewed", meaning it tends to have a long tail on one side or the other:
Why is it called negative skew? Because the long "tail"
is on the negative side of the peak.
Paul's Online Math Notes
Calculus I (Notes) / Derivatives / Derivatives of Inverse Trig Functions [Notes] [Practice Problems] [Assignment
Calculus I - Notes
Derivatives of In
Throwing dice - theory
Probability - coins experiment - coins theory - dice experiment - dice theory - for teachers
Sum of two dice
Other conditions with two dice
Either dice is a particular number
Neither dice is a particular number
COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding
Types of Mistakes
Summary Statistics for Skewed Distributions
Measure of Center
When we focus on the mean of a variabl
1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.5. Quantitative Techniques
126.96.36.199. Measures of Location
A fundamental task in many statistical analyses is to estimate
a location parameter for the distribution; i.e., to find a typical
Table of Contents | Home
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
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
3. Fridays Lecture: Do 9.4.33, 9.4.35, 9.4