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School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
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: Math For Business & Economics
Midterm 2 (info on site) No quiz this week Thursday night, same rooms as last time TLS Formulas from Chapter F F4: Amortization (Decreasing Annuity) Example: Find the monthly payment to pay off (amortize) a $100,000 loan over 40 years, at a rate of 8% (co
School: UConn
Course: Math For Business & Economics
Practice test posted on the site After class- download it tonight! 2 hour exam In lecture next week go over practice exam Mon/Wed Today F2 Compound Interest: Simple interest applies to principal F= P (1 +rt) = P+prt Compound interest applies to current
School: UConn
Course: Math For Business & Economics
Exam Two Review 2 and 10 b corrections on site Z-score and formulas from chapter f on website http:/www.math.uconn.edu/ClassHomePages/Math1070/math1070s14/ - info on rooms Math review 4/16 (TONIGHT) in ITE C80 5-7:30pm Ferrones Advice on exam: practice ex
School: UConn
Course: Math For Business & Economics
Midterm 2 (info on site) No quiz this week Thursday night, same rooms as last time TLS Formulas from Chapter F F4: Amortization (Decreasing Annuity) Example: Find the monthly payment to pay off (amortize) a $100,000 loan over 40 years, at a rate of 8% (co
School: UConn
Course: Math For Business & Economics
Practice test posted on the site After class- download it tonight! 2 hour exam In lecture next week go over practice exam Mon/Wed Today F2 Compound Interest: Simple interest applies to principal F= P (1 +rt) = P+prt Compound interest applies to current
School: UConn
Course: Math For Business & Economics
Next Week: Quiz on 2.2 Matrix multiplication and 1.3 solving a system of equations 1.3 Gaussian Elimination: Recall a linear system of equations, like 1. x + 2y = 20 2. 2x + y =16 One method to solve for x and y is substitution Use equation 2 to solve for
School: UConn
Course: Math For Business & Economics
F3 Increasing Annuities (sinking funds) Increasing Annuity: Savings account with equal payments each period, subject to compound interest Given: Interest rate r, compounded m times a year, with equal payments PMT, after n periods the balance is future val
School: UConn
Course: Math For Business & Economics
Midterm Two: Next Thursday April 17th Practice exam posted this week 4.6, 4.7, Chapter 5, (5.3, 5.4) Chap 6- (6.4) Chap F- Finance Quiz this week on 6.1-6.3 on Random variables histograms F1 Simple Interest and Discounts: Principal: The initial amount of
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: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
School: UConn
Course: Math For Business & Economics
Exam Two Review 2 and 10 b corrections on site Z-score and formulas from chapter f on website http:/www.math.uconn.edu/ClassHomePages/Math1070/math1070s14/ - info on rooms Math review 4/16 (TONIGHT) in ITE C80 5-7:30pm Ferrones Advice on exam: practice ex
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 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
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
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: Math For Business & Economics
Midterm 2 (info on site) No quiz this week Thursday night, same rooms as last time TLS Formulas from Chapter F F4: Amortization (Decreasing Annuity) Example: Find the monthly payment to pay off (amortize) a $100,000 loan over 40 years, at a rate of 8% (co
School: UConn
Course: Math For Business & Economics
Practice test posted on the site After class- download it tonight! 2 hour exam In lecture next week go over practice exam Mon/Wed Today F2 Compound Interest: Simple interest applies to principal F= P (1 +rt) = P+prt Compound interest applies to current
School: UConn
Course: Math For Business & Economics
Exam Two Review 2 and 10 b corrections on site Z-score and formulas from chapter f on website http:/www.math.uconn.edu/ClassHomePages/Math1070/math1070s14/ - info on rooms Math review 4/16 (TONIGHT) in ITE C80 5-7:30pm Ferrones Advice on exam: practice ex
School: UConn
Course: Math For Business & Economics
Next Week: Quiz on 2.2 Matrix multiplication and 1.3 solving a system of equations 1.3 Gaussian Elimination: Recall a linear system of equations, like 1. x + 2y = 20 2. 2x + y =16 One method to solve for x and y is substitution Use equation 2 to solve for
School: UConn
Course: Math For Business & Economics
F3 Increasing Annuities (sinking funds) Increasing Annuity: Savings account with equal payments each period, subject to compound interest Given: Interest rate r, compounded m times a year, with equal payments PMT, after n periods the balance is future val
School: UConn
Course: Math For Business & Economics
Midterm Two: Next Thursday April 17th Practice exam posted this week 4.6, 4.7, Chapter 5, (5.3, 5.4) Chap 6- (6.4) Chap F- Finance Quiz this week on 6.1-6.3 on Random variables histograms F1 Simple Interest and Discounts: Principal: The initial amount of
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
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: 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: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.6 Absolute Convergence and the Ratio and Root Tests We begin this section by considering a series whose terms are the absolute values of the terms of the original series. Definition ! is called absolutely convergent
School: UConn
Course: CALCULUS II
Chapter 8Further Applications to Integration 8.3Applications to Physics and Engineering In this section we consider applications of the integral calculus to both physics and engineering. In particular, the applications to these areas will involve hydrost
School: UConn
Course: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.1 Sequences A sequence can be thought of as a list of numbers written in a definite order. For example, 2, 4, 6, 8, 10. The sequence is said to be finite if there is a last number (e.g., in the example above) ! $ "
School: UConn
Course: CALCULUS II
Chapter 8Further Applications to Integration 8.5Probability As you know the probability that an event occurs is a number in the closed interval [0,1]that is, the probability that an event occurs can take on any number between 0 and 1 and including 0 or 1
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.8 Improper Integrals b In defining the definite integral f ( x)dx , the function f was assumed to be defined on a the closed interval [a, b]. We now extend the definition of the definite integral to consider an infinite
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.7 Approximate Integration b In evaluating a Definite Integral such as f ( x)dx , sometimes it is very difficult, or even a impossible, to find an antiderivative of f . As an example, it is impossible to evaluate the 1 2
School: UConn
Course: CALCULUS II
Chapter 6Applications of Integration 6.4Work Previously we learned that if ! ! represents the position of a particle at time ! then ! ! ! = !(!) that is, the first derivative of the position function represents the velocity of the particle at time ! and
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
Ch. 6 Applications of Integration 6.2 Volumes In this section we will learn how to use integrals to compute the volume of threedimensional solids. In doing so we will use two methodsthe method of disks and the method of washers. We begin with some simple
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.1 Integration by Parts In this chapter we will examine various techniques for evaluating integrals. We begin this section with a review all of the integration formulas we have studied as well as a brief review of the one
School: UConn
Course: CALCULUS II
Ch. 6 Applications of Integration 6.1 Areas Between Curves In a previous section we defined the area under the curve y = f (x) as the limit of the n Riemann sums, that is, A = lim f ( x *i )x . Next we defined the Definite Integral of n i =1 b f from a
School: UConn
Course: CALCULUS II
Chapter 9Differential Equations 9.1Modeling With Differential Equations Similar to what we studied in section 9.1, in this section we will examine DE that are used to model population growth including, the law of natural growth, the logistic equation, an
School: UConn
Course: CALCULUS II
11.4 The Comparison Tests In using the Comparison Tests to test for convergence or divergence we will compare a given series with a series that we know to be either convergent or divergent. For example, suppose we wanted to test whether the series is co
School: UConn
Course: CALCULUS II
University of Connecticut Department of Mathematics Math 1132 Practice Exam 1 Spring 2014 Name: Instructor Name: TA Name: Section: Discussion Section: Read This First! Please read each question carefully. Show ALL work clearly in the space provided. In o
School: UConn
Course: CALCULUS II
Let y(t) be the amount of alcohol in the vat after t minutes. Now, y(0) = (0.04)(500)= 20 gals, so initially the vat with 500 gals of beer contains 20 gals of alcohol. Now the amount of beer at all times in the vat remains at 500 gals so the %-age of alco
School: UConn
Course: CALCULUS II
Math 1132 Practice Final Exam Important Notice: To prepare for the nal exam, one should study the past exams and practice midterms (and homeworks, quizzes, and worksheets), not just this practice nal. A topic not being on the practice nal does not mean it
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 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 #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? Solution: 6! = 720. (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
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? Solution: There are 4 ways of choosing who goes into the rst room a
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: 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 #4 1. A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by x f (x) = Cxe 2 0 if x > 0 if x 0 what is the probability that the system funct
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: 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 Quiz #6 Question (10 points total) The density function of X is given by f (x) = a + bx2 0 if 0 x 1 otherwise. If E[X] = 3 , then nd a and b. 5 Solution: 1 x(a + bx2 ) dx = xf (x) dx = E[X] = So, if E[X] = 3 5, 0 a b + . 2 4 then 3 a b + = 2 4 5
School: UConn
Course: Probability
Math3160 Quiz #1 Question 1 (5 points total) Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place? Solution: To answer this question we need to count the number of ways that we can choose 2 people from
School: UConn
Course: Probability
Math3160 Quiz #5 Question 1 (10 points total) At time 0, a coin that comes up heads with probability p is ipped and falls to the ground. Suppose it lands on heads. At times chosen according to a Poisson process with rate , the coin is picked up and ipped.
School: UConn
Course: Mathematics For Business And Economics
Exam 1 Extra Practice Problems Math 1071Q Spring 2013 1. Find the domain of each of the following functions: (a) f (x) = 2x3 + 7x 5 (b) g(x) = x + 1 (c) h(x) = (d) k(x) = x2 +1 x2 1 3x x2 (e) j(x) = ln(2x + 3) 2. Solve the following equations for x: (a) 1
School: UConn
Course: Mathematics For Business And Economics
Math1071Q Fall 2013 Exam 2 review sheet 1. Find d (f (x) dx i f (x) = where 2 xix f (x) = ii f (x) = x1.4 xx f (x) = e3x (without using the chain rule) iii f (x) = 4 x x2 xxi f (x) = e3x (this time using the chain rule) iv f (x) = 1 ex 3 v f (x) = 4 3 ln
School: UConn
Course: Mathematics For Business And Economics
MATH 1071Q Fall 2013 Final Review 1. Dierentiate (a) F (x) = (4x3 + 5)2 (x4 2x)3 (b) H(z) = ln |3z 6 4z + 10| (c) S(x) = ln |x(x 4)| (d) y = e5x (x3 8x+5) 2. Evaluate (a) (b) (x3 5 x + 8)dx (x4 2x3 ) dx x (c) (9x 13)12 dx (d) xe(x 2 +1) dx 3. Find g(x) g
School: UConn
Course: Mathematics For Business And Economics
Math1071Q Fall 2013 Worksheet 1 (1.4 & 4.3) 1.4 (Domains of composite functions) 1 Note: 1.4 covers more than just composition of functions, but this is what we will concentrate on here. In the following questions you are given a pair of functions f and g
School: UConn
Course: Mathematics For Business And Economics
Math1071Q Fall 2013 Worksheet 2 (3.4) In the following questions, use the linear function f (c) + f (c)(x c) to approximate the given quantity. 1. 25.5 2. ln 0.95 3. 4. 1 0.96 3 1.1 5. e1.1 4. If the side of a square decreases from 4 inches to 3.8 inches,
School: UConn
Course: Math For Business & Economics
Midterm 2 (info on site) No quiz this week Thursday night, same rooms as last time TLS Formulas from Chapter F F4: Amortization (Decreasing Annuity) Example: Find the monthly payment to pay off (amortize) a $100,000 loan over 40 years, at a rate of 8% (co
School: UConn
Course: Math For Business & Economics
Practice test posted on the site After class- download it tonight! 2 hour exam In lecture next week go over practice exam Mon/Wed Today F2 Compound Interest: Simple interest applies to principal F= P (1 +rt) = P+prt Compound interest applies to current
School: UConn
Course: Math For Business & Economics
Next Week: Quiz on 2.2 Matrix multiplication and 1.3 solving a system of equations 1.3 Gaussian Elimination: Recall a linear system of equations, like 1. x + 2y = 20 2. 2x + y =16 One method to solve for x and y is substitution Use equation 2 to solve for
School: UConn
Course: Math For Business & Economics
F3 Increasing Annuities (sinking funds) Increasing Annuity: Savings account with equal payments each period, subject to compound interest Given: Interest rate r, compounded m times a year, with equal payments PMT, after n periods the balance is future val
School: UConn
Course: Math For Business & Economics
Midterm Two: Next Thursday April 17th Practice exam posted this week 4.6, 4.7, Chapter 5, (5.3, 5.4) Chap 6- (6.4) Chap F- Finance Quiz this week on 6.1-6.3 on Random variables histograms F1 Simple Interest and Discounts: Principal: The initial amount of
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: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.6 Absolute Convergence and the Ratio and Root Tests We begin this section by considering a series whose terms are the absolute values of the terms of the original series. Definition ! is called absolutely convergent
School: UConn
Course: CALCULUS II
Chapter 8Further Applications to Integration 8.3Applications to Physics and Engineering In this section we consider applications of the integral calculus to both physics and engineering. In particular, the applications to these areas will involve hydrost
School: UConn
Course: CALCULUS II
Ch. 11 Infinite Sequences and Series 11.1 Sequences A sequence can be thought of as a list of numbers written in a definite order. For example, 2, 4, 6, 8, 10. The sequence is said to be finite if there is a last number (e.g., in the example above) ! $ "
School: UConn
Course: CALCULUS II
Chapter 8Further Applications to Integration 8.5Probability As you know the probability that an event occurs is a number in the closed interval [0,1]that is, the probability that an event occurs can take on any number between 0 and 1 and including 0 or 1
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.8 Improper Integrals b In defining the definite integral f ( x)dx , the function f was assumed to be defined on a the closed interval [a, b]. We now extend the definition of the definite integral to consider an infinite
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.7 Approximate Integration b In evaluating a Definite Integral such as f ( x)dx , sometimes it is very difficult, or even a impossible, to find an antiderivative of f . As an example, it is impossible to evaluate the 1 2
School: UConn
Course: CALCULUS II
Chapter 6Applications of Integration 6.4Work Previously we learned that if ! ! represents the position of a particle at time ! then ! ! ! = !(!) that is, the first derivative of the position function represents the velocity of the particle at time ! and
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
Ch. 6 Applications of Integration 6.2 Volumes In this section we will learn how to use integrals to compute the volume of threedimensional solids. In doing so we will use two methodsthe method of disks and the method of washers. We begin with some simple
School: UConn
Course: CALCULUS II
Ch. 7 Techniques of Integration 7.1 Integration by Parts In this chapter we will examine various techniques for evaluating integrals. We begin this section with a review all of the integration formulas we have studied as well as a brief review of the one
School: UConn
Course: CALCULUS II
Ch. 6 Applications of Integration 6.1 Areas Between Curves In a previous section we defined the area under the curve y = f (x) as the limit of the n Riemann sums, that is, A = lim f ( x *i )x . Next we defined the Definite Integral of n i =1 b f from a
School: UConn
Course: CALCULUS II
Chapter 9Differential Equations 9.1Modeling With Differential Equations Similar to what we studied in section 9.1, in this section we will examine DE that are used to model population growth including, the law of natural growth, the logistic equation, an
School: UConn
Course: CALCULUS II
11.4 The Comparison Tests In using the Comparison Tests to test for convergence or divergence we will compare a given series with a series that we know to be either convergent or divergent. For example, suppose we wanted to test whether the series is co
School: UConn
Course: CALCULUS II
University of Connecticut Department of Mathematics Math 1132 Practice Exam 1 Spring 2014 Name: Instructor Name: TA Name: Section: Discussion Section: Read This First! Please read each question carefully. Show ALL work clearly in the space provided. In o
School: UConn
Course: CALCULUS II
Let y(t) be the amount of alcohol in the vat after t minutes. Now, y(0) = (0.04)(500)= 20 gals, so initially the vat with 500 gals of beer contains 20 gals of alcohol. Now the amount of beer at all times in the vat remains at 500 gals so the %-age of alco
School: UConn
Course: CALCULUS II
Math 1132 Practice Final Exam Important Notice: To prepare for the nal exam, one should study the past exams and practice midterms (and homeworks, quizzes, and worksheets), not just this practice nal. A topic not being on the practice nal does not mean it
School: UConn
Course: Mathematics For Business And Economics
Exam 1 Extra Practice Problems Math 1071Q Spring 2013 1. Find the domain of each of the following functions: (a) f (x) = 2x3 + 7x 5 (b) g(x) = x + 1 (c) h(x) = (d) k(x) = x2 +1 x2 1 3x x2 (e) j(x) = ln(2x + 3) 2. Solve the following equations for x: (a) 1
School: UConn
Course: Mathematics For Business And Economics
Math1071Q Fall 2013 Exam 2 review sheet 1. Find d (f (x) dx i f (x) = where 2 xix f (x) = ii f (x) = x1.4 xx f (x) = e3x (without using the chain rule) iii f (x) = 4 x x2 xxi f (x) = e3x (this time using the chain rule) iv f (x) = 1 ex 3 v f (x) = 4 3 ln
School: UConn
Course: Mathematics For Business And Economics
MATH 1071Q Fall 2013 Final Review 1. Dierentiate (a) F (x) = (4x3 + 5)2 (x4 2x)3 (b) H(z) = ln |3z 6 4z + 10| (c) S(x) = ln |x(x 4)| (d) y = e5x (x3 8x+5) 2. Evaluate (a) (b) (x3 5 x + 8)dx (x4 2x3 ) dx x (c) (9x 13)12 dx (d) xe(x 2 +1) dx 3. Find g(x) g
School: UConn
Course: Calculus 1
Math 1125Q Exam 1 Review Name: June 28, 2012 1. Find the domain of the following functions, using interval notation. 1 (a) f (x) = 2x 10 (b) f (x) = x2 16 (c) f (x) = ln(3x 1) x1 (d) f (x) = 2 x 4 2. Given f (x) = x3 1, g(x) = ln(x), h(x) = x nd and simp
School: UConn
Course: Calculus 1
Math 1125Q Exam 2 Review Name: July 5, 2012 1. The position of an object moving along a line is given by the function s(t) = 16t2 + 64t + 100. Find the average velocity of the object over the following intervals (a) [0, 3] (b) [0, 2] (c) [0, 1] (d) [0, h]
School: UConn
Course: Calculus 1
Math 1125Q Exam 2 Review Name: July 12, 2012 1. Find the vertical asymptotes of the following functions 1 (a) f (x) = 2 x 1 x2 + 3x + 2 (b) f (x) = x2 4 (c) f (x) = cot x tan(x) (d) f (x) = sin(x) 2. Find the horizontal asymptotes of the following functio
School: UConn
Course: Calculus 1
Math 1125Q Exam 4 Review Name: July 19, 2012 1. Use the limit denition to nd the the rst derivative of the following functions 1 (a) f (x) = 2 x (b) f (x) = x2 + 3x + 2 (c) f (x) = x 3 (d) f (x) = 2x + 1 2. Using parts (a)-(d) in #1, nd the equation of th
School: UConn
Course: ELEMENTARY DIFFERENTIAL EQUATION
Math 2410Q Final Review Name: May 1, 2013 1. Consider y = y 3 y 2 12y. For what values of y is y(t) at equilibrium? Increasing? Decreasing? 2. Give an example of (a) an autonomous dierential equation. (b) a separable dierential equation. (c) a linear dier
School: UConn
Course: Honors Calculus II
UConn Department of Mathematics Math 2130 Midterm I Spring 2014 PS ID: Name: I certify that all the work in this exam is my own (check box). This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem and in particular to perfor
School: UConn
Course: Honors Calculus II
12:00, Wed, March 12, 2014, MSB403 MATH2130S14-Honors Multivariable Quiz-6 PS ID: Name(Print): Show all work clearly and in order. You have 20 minutes to take this 10 point quiz. Your complete and correct personal information above carries 1 point. Good l
School: UConn
Course: Honors Calculus II
12:00, Wed, March 5, 2014, MSB403 MATH2130S14-Honors Multivariable Quiz-5 PS ID: Name(Print): Show all work clearly and in order. You have 15 minutes to take this 10 point quiz. Your complete and correct personal information above carries 1 point. Good lu
School: UConn
Course: Honors Calculus II
12:00, Wed, Feb.19, 2014, MSB403 MATH2130S14-Honors Multivariable Quiz-4 PS ID: Name(Print): Show all work clearly and in order. You have 10 minutes to take this 10 point quiz. Your complete and correct personal information above carries 1 point. Good luc
School: UConn
Course: Honors Calculus II
12:00, Wed, Feb. 12 , 2014, MSB403 MATH2130S14-Honors Multivariable Quiz-3 PS ID: Name(Print): Show all work clearly and in order. You have 15 minutes to take this 10 point quiz. Your complete and correct personal information above carries 1 point. Good l
School: UConn
Course: Honors Calculus II
12:00, Wed, Feb. 5 , 2014, MSB403 MATH2130S14-Honors Multivariable Quiz-2 PS ID: Name(Print): Show all work clearly and in order. You have 15 minutes to take this 10 point quiz. Your complete and correct personal information above carries 1 point. Good lu
School: UConn
Course: Honors Calculus II
12:00, Wed, Jan 29, 2014, MSB403 MATH2130S14-Honors Multivariable Quiz-1 PS ID: Name(Print): Show all work clearly and in order. You have 15 minutes to take this 10 point quiz. Your complete and correct personal information above carries 1 point. Good luc
School: UConn
Course: Honors Calculus II
Math 2130 Name: Homework 4 Due 9/20/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Derivatives and Integrals of Vectors (10 points) 1 t2 sin t cos
School: UConn
Course: Honors Calculus II
Math 2130 Name: Homework 3 Due 9/13/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Decompose a Vector (10 points) 1 2 2 0 Let u = and v = 3 1 . D
School: UConn
Course: Honors Calculus II
Math 2130 Name: Homework 2 Due 9/6/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Parallelism (10 points) Find all points on the curve x(t) = 4t, y
School: UConn
Course: Honors Calculus II
Math 2130 Name: Homework 1 Due 8/30/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Parameterize a Curve (10 points) Write a parameterization for th
School: UConn
Course: Honors Calculus II
Preparation for Exam I- MATH2110 Yichao Zhang Exam I: Date and place: 12:05pm-1:10pm, Feb 26, in class. Material covered: Lectures, quizzes, homework, and practice exam below. Policies: No calculators or other aids are allowed. Material for Exam: Section
School: UConn
Course: Calculus For Business And Economics
SPRING 2014 MATH 1152Q SECTION 2 HONORS CALCULUS II INFORMATION AND SYLLABUS Instructor: Alan Parry Email: alan.parry@uconn.edu Phone: 860-486-2362 Oce: MSB 233 Oce Hours: MWF 10:40am - 11:10am and 12:15pm - 1:15pm Classroom: MSB 403 Class Time: MWF 9:20a
School: UConn
Course: Calculus For Business And Economics
SPRING 2014 MATH 1152Q SECTION 2 HOMEWORK WORKSHEET 6 Name: Due Date: 28 March 2014 1. Sketch a direction eld for the dierential equation. Then use it to sketch three solutions curves. y = x y + 1. 2. Solve the dierential equations. (a) (y 2 + xy 2 )y = 1
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: CALCULUS II
Math 1132 HW 6.7 Fall 12 1. Dierentiate f (x) = ln(ln(4x) Solution: Use the chain rule: f (x) = 8 2. Evaluate 0 1 4 1 = ln 4x 4x x ln 4x 4x 1 dx x+1 Solution: Let u = x + 1. Then x = u 1 and du = dx. So we have 0 4x 1 dx = x+1 9 4(u 1) 1 du u 9 8 4u 5 du
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
09/10/2013' Intro to R Robert C. Zwick University of Connecticut Download R The software is freely available at:! http:/cran.r-project.org! Windows and Mac versions available Boot Up R version 3.0.1 (2013-05-16) - "Good Sport" Copyright (C) 2013 The R F
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 12 Count Dependent Variables Brian M. Hartman, PhD, ASA University of Connecticut 2 Poisson Distribution The Poisson distribution is used for counts and has probability mass function Pr = = , = 0,1,2, ! = ; = The Poisson distrib
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 11 Categorical Dependent Variables Brian M. Hartman, PhD, ASA University of Connecticut 2 Binary Dependent Variables We know how to handle categorical explanatory variables. What if you are interested in modeling a categorical respons
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 7 Modeling Trends Brian M. Hartman, PhD, ASA University of Connecticut 2 Definitions A process is a series of actions or operations that lead to a particular end. A stochastic process is a collection of random variables that quantify
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 1 Regression and the Normal Distribution Brian M. Hartman, PhD, ASA University of Connecticut 2 Galton (1885) Widely considered the birth of regression Galton looked at the heights of 928 adult children All female heights were multip
School: UConn
Course: Actuarial Statistics -enrollment Restrictions-see Catalog
MATH 3621: Chapter 6 Interpreting Regression Results Brian M. Hartman, PhD, ASA University of Connecticut 2 Interpreting Individual Effects Substantive/Practical Significance Does a 1 unit change in x imply an economically meaningful change in y? Stati
School: UConn
Course: Technical Writing For Actuaries
Aakash Patel Final Report Actuarial Staffing Report Contents: Introduction.2 Salary. 2 Benefits.4 Exam Costs. 5 Exam Raises.7 Hiring/Replacing.9 Conclusion. 13 Mr. CFO, I have put together a well-developed and clearly articulated report on the companys lo
School: UConn
Course: Math For Business & Economics
Exam Two Review 2 and 10 b corrections on site Z-score and formulas from chapter f on website http:/www.math.uconn.edu/ClassHomePages/Math1070/math1070s14/ - info on rooms Math review 4/16 (TONIGHT) in ITE C80 5-7:30pm Ferrones Advice on exam: practice ex
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 Quiz #6 Question (10 points total) The density function of X is given by f (x) = a + bx2 0 if 0 x 1 otherwise. If E[X] = 3 , then nd a and b. 5 Solution: 1 x(a + bx2 ) dx = xf (x) dx = E[X] = So, if E[X] = 3 5, 0 a b + . 2 4 then 3 a b + = 2 4 5
School: UConn
Course: Probability
Math3160 Quiz #1 Question 1 (5 points total) Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place? Solution: To answer this question we need to count the number of ways that we can choose 2 people from
School: UConn
Course: Probability
Math3160 Quiz #5 Question 1 (10 points total) At time 0, a coin that comes up heads with probability p is ipped and falls to the ground. Suppose it lands on heads. At times chosen according to a Poisson process with rate , the coin is picked up and ipped.
School: UConn
Course: MULTIVARIABLE CALCULUS
Math 2110Q Final Review Name: April 28, 2014 1. Given the points P (2, 0, 6) and Q(2, 8, 5) (a) Find the poosition vector equal to P Q . (b) Find 2 vectors with length 2 parallel to P Q . (c) Find the vector-valued function r(t) of the line segment P Q. 2
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 6 Solutions 1. A matrix A and its RREF B are given below. Find bases for N ul 2 4 2 4 1 0 6 2 6 3 B= 0 2 5 1 A= 3 8 2 3 0 0 0 A and Col A. 5 3 0 Solution It only takes one step to complete the row reduction process and get the RREF of A.
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 3 Solutions 1. Solve the following linear system and write the solution in parametric vector form. x1 + 2x2 3x3 = 5 2x1 + x2 3x3 = 13 x1 + x2 8 Solution 1 2 3 5 1 2 3 5 1 2 3 5 1 0 1 7 2 1 3 13 0 3 3 3 0 1 1 1 0 1 1 1 1 1 0 8 0 3 3 3 0 0
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz Name: Show all work. Answers without work or justication will not receive credit. 1. Solve the following linear system or show that it is inconsistent. Reduce the appropriate augmented matrix completely to reduced row echelon form. x1 3x3
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 2 Solutions 1. Determine if b is a linear combination of a1 , a2 , and a3 . 1 0 5 a1 = 2 , a2 = 1 , a3 = 6 , 0 2 8 2 b = 1 6 Solution 1 0 5 2 1 0 5 2 1 0 5 2 2 1 6 1 0 1 4 3 0 1 4 3 (RREF ) 0 2 8 6 0 2 8 6 0 0 0 0 This shows that the sy
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 8 Solutions 1. For each problem below, a matrix A is given. (The eigenvalues are also given in part b to save time, but you must determine the eigenvalues in part a.) Diagonalize each matrix, if possible; that is, nd a diagonal matrix D and
School: UConn
Course: Applied Linear Algebra
Math 2210 Test 2 Solutions Part I. 1. Compute the determinants of the following matrices using the indicated method. 3 2 0 0 7 4 3 5 (Cofactor expansion about any row or column you choose) a) (5 pts) 1 0 0 1 2 0 1 2 Solution Several rows and columns
School: UConn
Course: Applied Linear Algebra
Math 2210 Test 1 Solutions Part I 1. Consider the following linear system. x1 3x1 2x1 + 2x2 x2 2x2 5x3 5x3 2x3 + x4 + x4 = 1 = 1 = 1 a) (6 pts) Using Gaussian elimination, nd the solution(s) to this system, or conclude that it is inconsistent. Reduce t
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 5 Solutions 1. Compute the determinant of the following matrix by using cofactor expansions. You may choose any row or column for the expansion. 4 3 0 A= 6 5 2 9 7 3 Solution Using a cofactor expansion about row 1, we obtain the following.
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 4 Solutions 1. Determine whether or not the following matrix is invertible. If it is, nd the inverse. 3 0 0 0 A = 3 4 8 5 3 Solution 3 0 0 1 0 0 1 0 0 1/3 0 0 1 0 0 1/3 0 0 3 4 0 0 1 0 3 4 0 0 1 0 0 4 0 1 1 0 8 5 3 0 0 1 8 5 3 0 0 1 0 5
School: UConn
Course: Applied Linear Algebra
Math 2210 Quiz 7 Solutions 1. A matrix A and one of its eigenvalues is given below. Determine the eigenspace of A (or a basis for the eigenspace) corresponding to that eigenvalue. 4 1 1 2 , = 5 A = 2 3 3 3 2 Solution 1 1 1 1 1 1 row reduce A (5)I = A + 5I
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: Mathematics For Business And Economics
Math1071Q Fall 2013 Worksheet 1 (1.4 & 4.3) 1.4 (Domains of composite functions) 1 Note: 1.4 covers more than just composition of functions, but this is what we will concentrate on here. In the following questions you are given a pair of functions f and g
School: UConn
Course: Mathematics For Business And Economics
Math1071Q Fall 2013 Worksheet 2 (3.4) In the following questions, use the linear function f (c) + f (c)(x c) to approximate the given quantity. 1. 25.5 2. ln 0.95 3. 4. 1 0.96 3 1.1 5. e1.1 4. If the side of a square decreases from 4 inches to 3.8 inches,
School: UConn
Course: Multivariable Calculus
Math 2110 Due: Wednesday 9/12 Homework #1 1. Section 11.2, exercise 67 (on p. 702) Solution: Consider this picture: v w M3 M1 M2 u O a. It follows from the tip-to-tail denition of vector addition that u + v + w = 0. b. If M1 is the vector from the midpoin
School: UConn
Course: Multivariable Calculus
Math 2110 Due: Thursday, Sept 20 Homework #2 Instructions: Fully explain your answers, using complete sentences and gures if applicable. Please make sure that the work you hand in is neat and legible. 1. Section 11.7, exercise 60 (on page 749) Solution: (
School: UConn
Course: Multivariable Calculus
Math 2110 Due: Thursday, Oct 11 Homework #3 Solutions Instructions: Fully explain your answers, using complete sentences and gures if applicable. The assignment you hand in should be a nal draft. Make sure that it is legible and that your answers are clea
School: UConn
Course: Multivariable Calculus
Math 2110 Fall 2012 Due: Tues, Nov 6 Integrals Project Solutions Instructions: Fully explain your answers, using complete sentences and gures if applicable. The assignment you hand in should be a nal draft. Make sure that it is legible and that your answe
School: UConn
Course: Multivariable Calculus
Math 2110 Due: Thursday, Dec 6 Homework #5 Instructions: Fully explain your answers, using complete sentences and gures if applicable. The assignment you hand in should be a nal draft. Make sure that it is legible and that your answers are clearly marked.
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework 5 Problem 1. (Silvermans VIII: 8.1, 8.2) (a) Let K be a number eld, E/K and elliptic curve, m 2 and integer, Cl(K ) the ideal class group of K and 0 0 S = cfw_ MK : E has bad reduction at cfw_ MK : (m) = 0 MK . Assumi
School: UConn
Course: The Arithmetic Of Elliptic Curves
MATH 5020 - Elliptic Curves Homework 4 Problem 1 As you know, the elliptic curve y 2 = x3 +2x2 3x satises E (Q)[4] = Z/4ZZ/2Z. In previous exercises, it has been shown that Q(E [4]) = Q(i, 3) and Gal(Q(E [4])/Q) Z/2Z Z/2Z. = Z/4Z Z/2Z, In the rest of the
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework 3 (the exercise below) Problem 1 The elliptic curve y 2 = x3 + 2x2 3x satises E (Q)[4] = Z/4Z Z/2Z, i.e. the full 2-torsion is dened over Q and there is also a point of order 4 dened over Q. The goal of this exercise i
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework 2 and 3 - Word problems Note: At the beginning of each proof, the author is indicated. In most cases, I have only added some minor comments to the original submitted proof. P1-Hw2. (Proofs by Gagan Sekhon) Let E/Q be a
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework 2 (3.4 (use SAGE), 3.5, 3.8, and the exercise below) 3.4 Referring to example (2.4), express each of the points P2 , P4 , P5 , P6 , P7 , P8 in the form [m]P1 + [n]P3 with m, n Z. 3.5 Let E/K be given by a singular Weie
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework Chapter 3 (3.4 (use SAGE), 3.5, 3.8) 3.4 Referring to example (2.4), express each of the points P2 , P4 , P5 , P6 , P7 , P8 in the form [m]P1 + [n]P3 with m, n Z. Proof by Ryan Schwarz. Using SAGE and some trial and er
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework Chapter 2 (2.3, and 2.6) 2.3 (a) Prove proposition 2.6 for the special case of a non-constant map : P1 P1 . Proof (by Alvaro). Let : P1 P1 be a non-constant separable rational map. Thus, it is determined by ([x, 1]) =
School: UConn
Course: The Arithmetic Of Elliptic Curves
Math 5020 - Elliptic Curves Homework - Chapter 1 (1.3, 1.6) 1.3 Let V An be a variety given by a single equation. A point P V is nonsingular if and only if dimK mP /m2 = dim V, P where mP is the maximal ideal of P in the ane ring of V . Proof (by Alvaro a
School: UConn
Course: Actuarial Models
MATH 3634 - Actuarial Models Spring 2013 - Valdez Homework 2 due Wednesday, anytime before midnight, 1 May 2013 Total marks: 100 Please write your names and student numbers at the spaces provided: Student 1: Student ID: Student 2: Student ID: Follow these
School: UConn
Course: Actuarial Models
MATH 3634 - Actuarial Models Spring 2013 - Valdez Homework 1 Total marks: 100 due Friday, 22 February 2013, 6:00 PM Please write your name and student number at the spaces provided: Name: Student ID: Follow these instructions: There are ve (5) questions
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 4 Due 2/14/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Compute an Area (10 points) Compute the area of the region b
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 4 Due 2/14/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Compute an Area (10 points) Compute the area of the region bound
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 3 Due 2/7/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 FTC and Chain Rule (10 points) Let f1 (x), f2 (x) be dierenti
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 3 Due 2/7/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 FTC and Chain Rule (10 points) Let f1 (x), f2 (x) be dierentiable
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 2 Due 1/31/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Practice Your Riemann Sums (10 points) Use a regular partiti
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 2 Due 1/31/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Practice Your Riemann Sums (10 points) Use a regular partition i
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 1 Due 1/24/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Remember Your Limits (10 points) Calculate the following lim
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 1 Due 1/24/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Remember Your Limits (10 points) Calculate the following limits
School: UConn
Course: Mathematics For Business And Economics
csl N CO rt 4 (A ON .4 \i ) ')i I ! 0 n _L_i ~^ *i- Ki X ^ 6C o 03 U !i X^ CS3 -^ +. 'rO j x ^ -C \4. 4- cr 4- 4 I x ;i i >? >-/ > ^ -^ _a ~ -\J 761 : 10 ! ^ y. ^ * ^ (O >^ c X. VI cr ! > ^ 0 9 \? N) V s S5 -s O 5i ^ c* ^ *> ^ ^- ! t - -^51 - X ^3 v^ P S.
School: UConn
Course: Elementary Discrete Mathematics
Beginning Probability 1. Consider rolling 2 six-sided dice and taking the sum of their values. (hint: There are 36 possible outcomes) What is the probability of: (a) obtaining a sum of 6? Solution: There are 5 ways to roll a 6, and 36 possible outcomes wh
School: UConn
Course: Mathematics For Business And Economics
T " (v 'P i- (.A.D 05 -<p /-/ (p) I I <i G 5 3 "Q <v cs,/ ^ 41 v?> Jf!i ^ o C I >^ ' x a; /*~ u t x. Ii A Vo 0 OS a o <\ iJ 2S C o VL \ 0 * i 0 r a/ cs V-' W.y U- Q- Q\ ,| -t- /" / v J /* (J2) oz* per d e/vO x -t= -Wr 6 A H- \) O DQ p ex t-t Pro^t'i ~ R
School: UConn
Course: Mathematics For Business And Economics
I0 <r a -X. ' cfw_ O -iC) X =T j *' Jr Q <r S\7 -g . -t t rr Oo ^ -qr o x t - <f f 7 fX r to |( o TT^p ^> -n I- V* 2x N5 N> K s., u >? J i " ? X -J , ,. H A- r-o C.-C. CD 11 (\ x X ~-> It vP *\' *S-N N ,- "x ! VM -V W 4 (T1 \
School: UConn
Course: Elementary Discrete Mathematics
Math 1030 Spring 2013 Plurality and Run-o Methods 1. Twelve friends would like to see a movie, so they vote on their options. Their preferences are as follows: Dont be Afraid of the Dark Rise of the Planet of the Apes Our Idiot Brother 30 Minutes or Less
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 11 Due 4/11/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Converge or Diverge (10 points) Determine whether the following
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 10 Due 4/4/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Converge or Diverge (10 points) Determine whether the follow
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 9 Due 4/4/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Converge or Diverge (10 points) Determine whether the following s
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 9 Due 3/28/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Proving a Limit (10 points) Prove that lim n 1 n2 n 2 =1 1+8
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 9 Due 3/28/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Proving a Limit (10 points) Prove that 1 lim n 2 n n2 2 Proving
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 7 Due 3/14/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Trigonometric Integrals (10 points) Use the double-angle tri
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 7 Due 3/14/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Trigonometric Integrals (10 points) Use the double-angle trick d
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 7 Due 3/7/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Arclength (10 points) 3 Consider the curve y = ax 2 , 0 x b.
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 7 Due 3/7/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Arclength (10 points) 3 Consider the curve y = ax 2 , 0 x b. Dete
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 6 Due 2/28/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Compute a Hypervolume (10 points) Consider a cone living in
School: UConn
Course: Honors Calculus II
Math 1152 Name: Homework 6 Due 2/28/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Compute a Hypervolume (10 points) Consider a cone living in 4-di
School: UConn
Course: Honors Calculus II
Math 1152 Solutions Homework 5 Due 2/21/13 It goes without saying that you should show all work and clearly explain your reasoning. Do not use any electronic devices except to check your work. 1 Compute a Volume Two Ways (10 points) Consider the solid obt
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
School: UConn
Spring 2009 Math 2110Q, Section 02 Class meets MWF 11:00 am -12:15 pm in MSB 307. Text: J. Stewart, Multivariable Calculus: Early Transcendentals, 6th edition. Instructor: Wally Madych, MSB 308 O. Hours: MWF 10-11 am, 1-2 pm, and by arrangement. Cont
School: UConn
University of Connecticut Advanced Financial Mathematics Math 5660(324) Spring 2009 Classes: MWF: 1:00 1:50 MSB415 Instructor: James G. Bridgeman, FSA MSB408 Office Hours: M 11:00 12:00 860-486-8382 W 5:00 6:00 bridgeman@math.uconn.edu Th/F 10:00