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School: UConn
1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 2 x1 7 x2 = 5 1
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.4 Integration of Rational Functions by Partial Fractions In this section we will learn how to integrate rational functions by expressing them as a sum of simpler functions, called partial fractions, that we know how to in
School: UConn
Course: CALCULUS II
Chapter(11(Review(Notes( ( Chapter(11(is(on(Infinite(Sequences(and(Series.(We(begin(with(Sequences.( ( Sequences( Simply(put,(a(mathematical(sequence(is(a(set(of(numbersfor(example,(2,(4,(6,(8,(10( (designated(as(a(finite(sequence)(or(1,(,(,.(designated(a
School: UConn
Course: CALCULUS II
Chapter 10Parametric Equations and Polar Coordinates 10.4Areas and Lengths in Polar Coordinates In this section we will examine the area of a region whose boundary is given by a polar equation. For example, suppose we were interested in finding the area
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.4 Integration of Rational Functions by Partial Fractions In this section we will learn how to integrate rational functions by expressing them as a sum of simpler functions, called partial fractions, that we know how to in
School: UConn
Course: CALCULUS II
Chapter(11(Review(Notes( ( Chapter(11(is(on(Infinite(Sequences(and(Series.(We(begin(with(Sequences.( ( Sequences( Simply(put,(a(mathematical(sequence(is(a(set(of(numbersfor(example,(2,(4,(6,(8,(10( (designated(as(a(finite(sequence)(or(1,(,(,.(designated(a
School: UConn
Course: CALCULUS II
Chapter 10Parametric Equations and Polar Coordinates 10.4Areas and Lengths in Polar Coordinates In this section we will examine the area of a region whose boundary is given by a polar equation. For example, suppose we were interested in finding the area
School: UConn
Course: CALCULUS II
Chapter 10Parametric Equations and Polar Coordinates 10.1Curves Defined By Parametric Equations Suppose that !"#! are both given as functions of a third variable ! (called a parameter) by the equations ! = !(!) and ! = !(!) (called parametric equations).
School: UConn
Course: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.2 Series % Suppose we are given some infinite sequence !"# $ #&' = "' , ") , "* , , "# , and were asked to add up its terms, that is, "' + ") , + + "# , This new expression, that is, "' + ") , + + "# , is called an
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Initial Assessment Essay Risk is everywhere in the world today. With risk comes uncertainty. Not knowing what the future holds can be very daunting, especially in the business world. However, this is where actuaries excel. Actuaries are exper
School: UConn
Course: CALCULUS II
Math 1132 1. HW 5.5 / 6.2 Fall 12 4x3 dx 1 12x4 Solution: Let u = 1 12x4 . Then du = 48x3 dx and 2. du = 4x3 dx. So we have 12 1 4x3 du dx = 12 u 1 12x4 u 1 = +C 12 1/2 1 1 12x4 + C = 6 dx 9x + 1 Solution: Let u = 9x + 1. Then du = 9dx and dx 1 du = 9x +
School: UConn
Course: CALCULUS II
Math 1132 HW 6.3 Fall 12 1. Use the general slicing method to nd the volume of the solid with a base dened by the curve y = 12 sin x and the interval [0, ] on the x-axis. The cross-sections of this solid are squares perpendicular to the x-axis with bases
School: UConn
Course: CALCULUS II
Math 1132 HW 7.1 Fall 12 xe9x dx 1. Use integration by parts to evaulate Solution: Let u = x and dv = e9x dx. Then du = dx and v = 1/9e9x . By the integration by parts formula: udv = uv vdu gives xe9x dx = 1 9x 1 xe 9 9 e9x dx 1 9x 1 1 9x xe e +C 9 9 9
School: UConn
Course: CALCULUS II
Math 1132 HW 6.5 Fall 12 1. Find the arc length of the line y = 2x+4 on the interval [0, 3] using calculus Solution: Using the formula for the length of a curve on an interval: b L= 1 + f (x)dx a We get 3 1 + 22 dx L= 0 =3 5 2. Find the length of the curv
School: UConn
Course: CALCULUS II
Math 1132 HW 6.6 Fall 12 1. A 170 lb person compresses a bathroom scale 0.170 in. If the scale obeys Hookes law, how much work is done compressing the scale if a 100 lb person stands on it? Solution: First we need to solve for k: 170 = k(.17) gives k = 10
School: UConn
Course: CALCULUS II
Math 1132 HW 7.2 Fall 12 2 sin2 xdx 1. Solution : Use the half-angle formula: sin2 (x) = 1 (1 cos(2x) 2 So 2 sin2 xdx = (1 cos(2x)dx =x 2. 1 sin(2x) + C 2 cos3 (x)dx Solution : Split o a cos(x), giving cos3 (x) = cos(x) cos2 (x) Now use the trig identity
School: UConn
Course: Probability
University of Connecticut Department of Mathematics University of Connecticut Department of Mathematics Math 3160 Exam 1, Fall 2013 Duration: 50 minutes Name: Section: Question Points 1 10 2 10 3 10 4 10 5 10 6 10 Total: Score 50 1. You should attempt 5 o
School: UConn
Course: Probability
University of Connecticut Department of Mathematics University of Connecticut Department of Mathematics Math 3160 Exam 2, Fall 2013 Duration: 50 minutes Name: Section: Question Points 1 10 2 10 3 10 4 10 5 10 6 10 Total: Score 50 1. You should attempt 5 o
School: UConn
Course: Probability
Math3160 Quiz #2 Question 1 (4 points total) A pair of fair dice is rolled. What is the probability that the second die lands on a higher value than does the rst? Solution: Let E be the event that the second die rolled has a higher number than the rst. Th
School: UConn
Course: Probability
Math3160 Quiz #3 Question 1 (5 points total) Two cards are randomly chosen without replacement from an ordinary deck of 52 cards. Let B be the event that both cards are aces, let As be the event that the ace of spades is chosen, and let A be the event tha
School: UConn
Course: Probability
Math3160 Quiz #4 Question 1 (5 points total) An insurance company writes a policy to the eect that an amount of money A must be paid if some event E occurs within a year. If the company estimates that E will occur within a year with probability p, what sh
School: UConn
Course: Probability
Math3160 Worksheet #1 1. Some simple combinatorial problems to get us started: (a) In how many ways can 3 boys and 3 girls sit in a row? (b) In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together? (c) In ho
School: UConn
Course: Probability
Math3160 Worksheet #2 1. Suppose I have 4 people who are going to spend the night at a hotel in two rooms, with two people in each room. How many ways are there for the people to pair up? 2. Suppose 20 people are gathered together and consist of 10 marrie
School: UConn
Course: Probability
Math3160 Worksheet #3 1. Suppose that it takes at least 9 votes from a 12 member jury to convict a defendant. Suppose also that the probability that a juror votes a guilty person innocent is 0.2, whereas the probability that the juror votes an innocent pe
School: UConn
Course: Complex Function Theory I
Study guide for Ph.D. Examination in Complex Analysis (Math 5120) Holomorphic (analytic) functions: (1) (2) (3) (4) (5) Statement of the Jordan curve theorem and the notion of simple rectiable curves. The Riemann sphere. The Cauchy-Riemann equations. Powe
School: UConn
Study Guide for Risk Theory Prelim (MATH5637) 1. Modeling with random variables a. pf, pdf, cdf, ddf, hazard rate, moments (and related measures), quantiles b. generating functions and transforms: moment-, probability-, cumulant-; Fourier (characteristic)
School: UConn
Course: CALCULUS II
CourseDescription 1132Q.CalculusII Fourcredits.Prerequisite:MATH1121,1126,1131,or1151,oradvancedplacementcredit forcalculus(ascoreof4or5ontheCalculusABexamorascoreof3orbetteronthe CalculusBCexam).Recommendedpreparation:AgradeofCorbetterinMATH1121 or1126or
School: UConn
Course: CALCULUS II
CourseDescription 1132Q.CalculusII Four credits.Prerequisite:MATH 1121,1126,1131,or 1151,or advancedplacementcreditfor calculus(a scoreof 4 or 5 on the CalculusAB examor a scoreof 3 or betteron theCalculusBC exam). Recommendedpreparation:A gradeof C- or b
School: UConn
Course: Problem Solving
Math 1020Q Group Projects (Great American Road Trip) Collectively as a class, we will plan a 10-week driving trip around the continental United States, also known as the Great American Road Trip. Each group will have one of the regions on the back and the
School: UConn
Course: Problem Solving
PROBLEM SOLVING MATH 1020Q Section 003 SYLLABUS Meeting Times: MWF, 2:00pm 2:50pm in MSB219 Textbook: PProblem SSSolving, 2nd Edition, by DeFranco and Vinsonhaler Ben Brewer, MSB201 Email: benjamin.a.brewer
School: UConn
Course: Problem Solving
PROBLEM SOLVING MATH 1020Q Section 002 SYLLABUS Meeting Times: MWF, 10:00am 10:50am in MSB303 Textbook: PProblem SSSolving, 2nd Edition, by DeFranco and Vinsonhaler Ben Brewer, MSB201 Email: benjamin.a.brew
School: UConn
Course: Financial Mathematics I
University of Connecticut Financial Mathematics I - Math 2620/5620 Syllabus - Fall 2011 (revised 9/12/2011) Welcome to Financial Math! This is an important foundation course in actuarial science and finance, with two principal goals for students: The firs