# TA: Sum as n goes from 0 to infinity, x minus 2 to the n over n. What's the center?

Save this PDF as:

Size: px
Start display at page:

Download "TA: Sum as n goes from 0 to infinity, x minus 2 to the n over n. What's the center?"

## Transcription

1 MAT Calculus II TA: Sum as n goes from 0 to infinity, x minus 2 to the n over n. What's the center? Student: Two. TA: Two. Why is the center 2? Student: Because of when it's equal to 0. TA: Yeah, taking x minus 2 to the n, when is that equal to 0? What makes my term 0? Two. So, x equals 2 is the center. What is the radius? How do I find the radius? Uh, like Katie said, uh, absolute ratio test. The limit as n goes to infinity, absolute value of an plus 1 over an, limit as n goes to infinity, absolute value of x minus 2 to the n, over n plus 1. And over n plus 1 over x minus 2 to the n over n. And what do I get when I simplify? Student: x minus 2 times n over n plus 1. TA: Okay. So I get limit as n goes to infinity. This x minus 2 to the n will cancel with most of the copies of x minus 2 in the numerator. So you have absolute value of x minus 2 times n over n plus 1. And what is that limit? Student: The absolute value of x minus 2. TA: Yes, when I take the limit this term goes to 1 so I'm left with absolute value of x minus 2. And again absolute ratio test guarantees convergence when my limit is less than 1. So, when is this less than 1? What's my radius of convergence? Student: Two. TA: My center is 2. Student: One. TA: The radius of convergence is 1. Um, and what's the interval of convergence? When is x, absolute value of x minus 2 less than 1? Student: Between 1 and 3? TA: Between 1 and 3. And, again, I don't know if I include 1 or 3 yet, I need to check the endpoints individually. So, how do I find the radius? I get it into a form, just absolute value of a single multiple of x. There's no coefficient of x other than 1. x has a coefficient of 1 and then it's less than the radius. And I assume you can solve absolute values, this is a calc II class. So, what happens at the endpoints? What happens at x equals 1? What series do I have at x equals 1?

2 Student: Alternating harmonic. TA: It's the alternating harmonic. Does the alternating, ehh, does the alternating harmonic series converge or diverge? Student: Converge. TA: It converges. How so? It's an alternating series, so is it conditional or absolute convergence? Conditional, does the alternating series converge conditionally or doe sit converge absolutely? Student: Absolutely? TA: Ah, yeah, guess not. Um, if I take absolute values of the alternating harmonic series, make all the terms positive. What series do I get? Student: Harmonic. TA: The harmonic series, good. Does the harm, does the harmonic series converge or diverge? Student: Diverges. TA: It diverges. So, I have the alternating harmonic series. It converges, so 1 is included, the series, the power series does converge at x equals 1. But if I take everything absolute value, it diverges. So it's conditional convergence. Ah, conditional, c-o-n-v-e-r-g-e. So it converges conditionally. It has conditional convergence at x equals 1. How about at x equals 3? What series do I have if x equals 3? Student: Harmonic series. TA: The harmonic series. And as Joe just said, the harmonic series diverges. So, at x equals 3, this power series does not converge. So my interval of convergence is closed 1 to open 3. And I should see it diverges at x equals 3. So are there questions on problem 5? Okay, problem 6. And the reason I'm going over problems 5 and 6 is because you should expect problems like these on the final exam. Okay? These are good questions for a final and will cover up through, in fact the final will cover up through the end of chapter 10. Okay? So, problem number 6. I give you two power series and I apologize greatly, um, one of the power series that I gave you is not quite right. Did anyone pick that up? Oh. What's the power series for e to the x? Student: Isn't it x squared over 2? TA: It's x squared over 2. Student: Over 2 factorial?

3 TA: Over 2 factorial, yes. Um, fortunately for me the only time that that made a difference in peoples' answers was either if they got it completely right or if they missed some other things as well. Ah, so that didn't really effect point values which was lucky for me because typos on exams can change point values students would get. So, e to the x is 1 plus x plus x squared over 2 factorial plus x cubed over 3 factorial, plus x to the 4th over 4 factorial plus and so on. Um, I go up to the 7th term there, fine. Tan inverse of x is x minus x cubed over 3 plus x to the 5th over 5 minus x to the 7th over 7 and so on. For 1, sorry negative 1 less than x less than 1. The radius of convergence for this power series is 1. It's centered at 0 and it does not include the endpoints. Okay? Whereas the radius of convergence for e to the x is infinite. It's the whole real line. So for tan inverse of x there actually is a significance of convergence that you may have to worry about. Um, although no one picked that up on part b, I believe. Oh well. Ah, so part a. Find the first 4 non-zero terms the power series expansion for x e to the 2 x. How would I do that? Katie? Student: For every x and e to the x, you put in 2x. TA: Okay. Student: And then you'd multiply each of those by x. TA: Right. I have, so what Katie said is that I have x times this series except wherever I see an x I put in 2x. Here is my power, there's my exponent, so I plug that in. So, 1 plus 2x plus, what's my next term? Student: 4x squared. TA: 4x squared. So, it's the parenthesis, 2x squared. So, the 2 is getting squared as well. Many people got, I think, like 6 or 7 points on this problem, I think, because they did not square and cube this 2. 2x plus 2 x squared plus either 2x cubed or 4x cubed depending on how it's, this was the way that it was written according to my typo because I did not have that divide by 2 there. But this is what it really should be. I apologize for that. And then 8 6 is 4/3 x cubed times x is x to the 4th. So, that's a. Do, are there any questions about part a? MAT 296 Calculus II TA: Alright. Now, I'd actually like to do 10.8 before we do 10.7 if that's all cool with you all. Is that alright?

4 Students: Yeah. TA: Yeah? Student: On like the first few problems where they said like, there was like a first, it was like 8, 8, 1, 5. TA: Yeah. Student: I don't understand how they like divide, multiply like infinite... TA: We talked about that briefly and basically what we said is that you just have to collect up the terms in the right power. So, I'd like to actually do one of these. Number 3. Student: Like 3 I can sort of see, but like 1, I have no clue on. TA: Yeah, um, 1 I wouldn't do by dividing. One if I were you, I'd do by taking derivatives. And that actually, the taking derivatives actually writing out the McLoren series and the Taylor's series. That is what I think is more important than being able to divide and multiply big power series, but multiplying makes more sense, so we could look at number 3 because that was a product of e to the x and sin x. We can look at that one real quick just to get an idea what's going on. Did you, did you get 3 or did you have an idea about 3? Student: Yeah, you try and FOIL it out, but... TA: And you FOIL it out and you figure out what terms give you what degree terms and you can pretty much figure out what the terms are going to be because they're aren't that many possibilities of, of products of those terms getting up to degree 5. So you really don't have that much work to do. So, if we write this out real quick. e to the x we said was, ah, 1 plus x plus x squared over 2 factorial plus x cubed over 3 factorial, x 4 over 4 factorial, x 5 over 5 factorial plus so on and so forth. I stopped at 5 because they asked me for terms up to degree 5. So, I'm to list all the terms of this up to degree 5 and I know I want to list sin x. Sin x? Is that what they said? Sin x up to degree 5. So, this was x minus x cubed over 3 factorial plus x 5 over 5 factorial minus so on and so forth. So then you just have to figure out when I multiply these things, these two things together which terms give me terms of degree 5 or less. Well, x times all of these guys up to degree 4 gives me terms of 5 or less. So I want to do x times 1 plus x plus x squared over 2 plus x cubed over 6 plus x 4 over 24. Or something. Sure. Does that make sense? If I multiply this x by the next term I get a degree 6 term. They only wanted up to degree 5. And then

5 I can take this negative x cubed and multiply that by 1, 2, these 3. Because if I multiply it by the next one I get a degree 6 term. So, I guess minus x cubed over 3 factorial times 1 plus x plus x squared over 2. And then plus the degree 5 term times just 1. Is that the entire product of e to the x sin x? No. There's a whole bunch of other stuff that comes after it. But these are all the possible terms that have degree 5 or less. Because the only thing I didn't multiply was x 5 times the rest of these guys which all have degree bigger than 5 or any later terms times all of these guys, which all have degrees bigger than 5. So you multiply these all out, collect up terms, you'll get the answer in the back of the book. For division you do kind of a similar thing, with long division. I didn't really want to get into it. I prefer if you did number 1, you did not do it by dividing sine by cosine. I think that's the harder way to do that problem., I would do it by taking the sum of the derivatives of the tangent because that's really what I'm going to be asking for on the tests and quizzes from now on which amounts to today's test and the final. So, it's like a hint or something.

### A power series about x = a is the series of the form

POWER SERIES AND THE USES OF POWER SERIES Elizabeth Wood Now we are finally going to start working with a topic that uses all of the information from the previous topics. The topic that we are going to

### Some Notes on Taylor Polynomials and Taylor Series

Some Notes on Taylor Polynomials and Taylor Series Mark MacLean October 3, 27 UBC s courses MATH /8 and MATH introduce students to the ideas of Taylor polynomials and Taylor series in a fairly limited

### (- 7) + 4 = (-9) = - 3 (- 3) + 7 = ( -3) = 2

WORKING WITH INTEGERS: 1. Adding Rules: Positive + Positive = Positive: 5 + 4 = 9 Negative + Negative = Negative: (- 7) + (- 2) = - 9 The sum of a negative and a positive number: First subtract: The answer

### BBC LEARNING ENGLISH 6 Minute English Is student life all good?

BBC LEARNING ENGLISH 6 Minute English Is student life all good? NB: This is not a word-for-word transcript Hello and welcome to 6 Minute English. I'm and I'm. Hello. Hello,. You went to university, didn't

### Call Scenarios. Tell them how you'll help them turn their transformation into cash.

Call Scenarios 1st Call Goals Introduce yourself and remind them they provided their phone number when they ordered their product. Identify yourself as a Team Beachbody Coach Explain that this is about

### Algebra. Exponents. Absolute Value. Simplify each of the following as much as possible. 2x y x + y y. xxx 3. x x x xx x. 1. Evaluate 5 and 123

Algebra Eponents Simplify each of the following as much as possible. 1 4 9 4 y + y y. 1 5. 1 5 4. y + y 4 5 6 5. + 1 4 9 10 1 7 9 0 Absolute Value Evaluate 5 and 1. Eliminate the absolute value bars from

### (Refer Slide Time: 2:03)

Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 11 Models of Industrial Control Devices and Systems (Contd.) Last time we were

### 731-04-joel_maloff-phone.com-cloud_based_phone_service Page 1 of 5

731-04-joel_maloff-phone.com-cloud_based_phone_service Page 1 of 5 Ranked the #1 radio show in the Boston Market in its time-slot, and with more than 5,500,000 Podcast downloads, Tech Talk With Craig Peterson

### Everyone cringes at the words "Music Theory", but this is mainly banjo related and very important to learning how to play.

BLUEGRASS MUSIC THEORY 101 By Sherry Chapman Texasbanjo The Banjo Hangout Introduction Everyone cringes at the words "Music Theory", but this is mainly banjo related and very important to learning how

### Chorus (x2) Chorus (x2)

Inequalities Algebra 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. Mr. Queen,

### Name: ID: Discussion Section:

Math 28 Midterm 3 Spring 2009 Name: ID: Discussion Section: This exam consists of 6 questions: 4 multiple choice questions worth 5 points each 2 hand-graded questions worth a total of 30 points. INSTRUCTIONS:

TheFourierTransformAndItsApplications-Lecture08 Instructor (Brad Osgood):We're on? Okay. So today first of all, any questions? Anything on anybody's mind? If you brought your problem sets with you, you

### Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

### Week 13 Trigonometric Form of Complex Numbers

Week Trigonometric Form of Complex Numbers Overview In this week of the course, which is the last week if you are not going to take calculus, we will look at how Trigonometry can sometimes help in working

### CALL 1 Dispatch: Santa Fe regional dispatch this is Daniel. Hotel desk: Hi Daniel, I'm calling from the El Dorado Hotel and uh we have a guest that

CALL 1 Dispatch: Santa Fe regional dispatch this is Daniel. Hotel desk: Hi Daniel, I'm calling from the El Dorado Hotel and uh we have a guest that has been partying in their room. They've been warned

### Calculating Logarithms By Hand

Calculating Logarithms By Hand W. Blaine Dowler June 14, 010 Abstract This details methods by which we can calculate logarithms by hand. 1 Definition and Basic Properties A logarithm can be defined as

### Math Matters: Why Do I Need To Know This? 1 Probability and counting Lottery likelihoods

Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Four 1 Probability and counting Lottery likelihoods Objective: To demonstrate the

### Chapter 13: Polynomials

Chapter 13: Polynomials We will not cover all there is to know about polynomials for the math competency exam. We will go over the addition, subtraction, and multiplication of polynomials. We will not

### To discuss this topic fully, let us define some terms used in this and the following sets of supplemental notes.

INFINITE SERIES SERIES AND PARTIAL SUMS What if we wanted to sum up the terms of this sequence, how many terms would I have to use? 1, 2, 3,... 10,...? Well, we could start creating sums of a finite number

Module 6.3 Client Catcher The Sequence (Already Buying Leads) Welcome to Module 6.3 of the Client Catcher entitled The Sequence. I recently pulled over 300 of the local lead generation explosion members

### Next Generation Tech-Talk. Cloud Based Business Collaboration with Cisco Spark

Next Generation Tech-Talk Cloud Based Business Collaboration with Cisco Spark 2 [music] 00:06 Phil Calzadilla: Hello, hello! Welcome. This is Phil Calzadilla founder and CEO of NextNet Partners, and I'd

### Corinne: I m thinking of a number between 220 and 20. What s my number? Benjamin: Is it 25?

Walk the Line Adding Integers, Part I Learning Goals In this lesson, you will: Model the addition of integers on a number line. Develop a rule for adding integers. Corinne: I m thinking of a number between

### Okay, good. He's gonna release the computers for you and allow you to log into NSLDS.

Welcome to the NSLDS hands-on session. My name is Larry Parker. I'm from the Department of Education NSLDS. Today, I have with me a whole host of folks, so we're gonna make sure that if you have any questions

### Inverse Circular Function and Trigonometric Equation

Inverse Circular Function and Trigonometric Equation 1 2 Caution The 1 in f 1 is not an exponent. 3 Inverse Sine Function 4 Inverse Cosine Function 5 Inverse Tangent Function 6 Domain and Range of Inverse

### Absolute Value of Reasoning

About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection

### Jenesis Software - Podcast Episode 3

Jenesis Software - Podcast Episode 3 Welcome to Episode 3. This is Benny speaking, and I'm with- Eddie. Chuck. Today we'll be addressing system requirements. We will also be talking about some monitor

### PRICING COMMERCIAL PROPERTY

MODULE 3 Remember I said that in the earlier part of this course that we would use interest only loans in order to keep things simple? Well, really, how easy would it be to get an interest only loan in

### Simple Regression Theory II 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

### Health Care Vocabulary Lesson

Hello. This is AJ Hoge again. Welcome to the vocabulary lesson for Health Care. Let s start. * * * * * At the beginning of the conversation Joe and Kristin talk about a friend, Joe s friend, whose name

### MITOCW watch?v=55oxxe_ix2o

MITOCW watch?v=55oxxe_ix2o The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To

### >> My name is Danielle Anguiano and I am a tutor of the Writing Center which is just outside these doors within the Student Learning Center.

>> My name is Danielle Anguiano and I am a tutor of the Writing Center which is just outside these doors within the Student Learning Center. Have any of you been to the Writing Center before? A couple

### Put on the Full Armor of God

Subject: ARMOR Author: Bob Snook Put on the Full Armor of God ARMOR 7'1m2f Put on the full armor of God (scene: three chairs side-by-side or couch facing audience, end table with phone, candy dish, TV

### (2 4 + 9)+( 7 4) + 4 + 2

5.2 Polynomial Operations At times we ll need to perform operations with polynomials. At this level we ll just be adding, subtracting, or multiplying polynomials. Dividing polynomials will happen in future

### A: We really embarrassed ourselves last night at that business function.

Dialog: VIP LESSON 049 - Future of Business A: We really embarrassed ourselves last night at that business function. B: What are you talking about? A: We didn't even have business cards to hand out. We

### Jenesis Software - Podcast Episode 2

Jenesis Software - Podcast Episode 2 All right, welcome to episode two with Chuck, Eddie, And Benny. And we're doing some technical talk today about network speed on episode two. Let's talk about, guys,

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 5 Subtracting Integers

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 5 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

### Jared Roberts (PelotonU)

p.1 Jared Roberts (PelotonU) Jared Roberts: Hello Dave. David Cutler: Hey, is this Jared? Jared: Yes, it is, how are you doing? David: I'm doing great, Jared. Thank you so much for speaking with me, I

### MATH 2300 review problems for Exam 3 ANSWERS

MATH 300 review problems for Exam 3 ANSWERS. Check whether the following series converge or diverge. In each case, justify your answer by either computing the sum or by by showing which convergence test

### Conference Call with Deputy Undersecretary Robert Shireman of the U.S. Department of Education. May 29, :45 AM ET

Deputy Undersecretary Robert Shireman of the U.S. Department of Education At this time all participants' lines will be in a listen-only mode for the duration of today's presentation. I'd now like to turn

### Taylor Polynomials and Taylor Series Math 126

Taylor Polynomials and Taylor Series Math 26 In many problems in science and engineering we have a function f(x) which is too complicated to answer the questions we d like to ask. In this chapter, we will

### Polynomial Expression

DETAILED SOLUTIONS AND CONCEPTS - POLYNOMIAL EXPRESSIONS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! PLEASE NOTE

### FELIX: (Staring at the door) That's funny, isn't it? They think we're happy. They really think we're enjoying this. They don't know what it's like.

Act Two SCENE I.Apt It is immaculately clean. No, not clean. Sterile! Spotless! Not a speck of dirt can be seen No laundry bags, no dirty dishes, no half-filled glasses. Suddenly FELIX appears from the

### Solving a System of Equations

11 Solving a System of Equations 11-1 Introduction The previous chapter has shown how to solve an algebraic equation with one variable. However, sometimes there is more than one unknown that must be determined

### Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.

Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating

### BBC LEARNING ENGLISH 6 Minute English Asking the right questions

BBC LEARNING ENGLISH 6 Minute English Asking the right questions NB: This is not a word-for-word transcript Hello and welcome to 6 Minute English. I'm and I'm. Now, I'm a big fan of chat shows, as you

### Chapter 2 Formulas and Decimals

Chapter Formulas and Decimals Section A Rounding, Comparing, Adding and Subtracting Decimals Look at the following formulas. The first formula (P = A + B + C) is one we use to calculate perimeter of a

### 14.01SC Principles of Microeconomics, Fall 2011 Transcript Lecture 3: Elasticity

14.01SC Principles of Microeconomics, Fall 2011 Transcript Lecture 3: Elasticity The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to

### POLAR COORDINATES DEFINITION OF POLAR COORDINATES

POLAR COORDINATES DEFINITION OF POLAR COORDINATES Before we can start working with polar coordinates, we must define what we will be talking about. So let us first set us a diagram that will help us understand

### Profiles of Mechanical Engineers

Profiles of Mechanical Engineers Jeffrey P. Martin, P.E. Product Design Engineer Ford Motor Company Dearborn, MI Education: MS, Mechanical Engineering, Washington University BS, Mechanical Engineering,

### DECEMBER WHAT TO DO WHEN THE PLANNED ACTIVITY FALLS APART (or

1 DECEMBER WHAT TO DO WHEN THE PLANNED ACTIVITY FALLS APART (or Why You Should Have a Plan B) Music Full then under Welcome, everyone, to our ScoutCast for December. With all the holidays and end-of-the-year

### Wendy Barrales: So show me what you're working on, which question are you on?

One-on-One Conferences Video Transcript Wendy So show me what you're working on, which question are you on? Number six. It's just that I'm having a problem with number six because I don't know what foreshadowing

### IT Audit. 15301 Dallas Parkway, Suite 960 Addison, Texas 75001- Phone: 214.545.3965 Fax: 214.545.3966 www.bkmsh.com

Radio Host: Every Wednesday BKM Sowan Horan comes in here, today we are so blessed to have Rick Sowan and Kevin Rockecharlie in here from IT Audit, did I get the company right? Rick Sowan: Correct Yes

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

### No Solution Equations Let s look at the following equation: 2 +3=2 +7

5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are

### 22 Matrix exponent. Equal eigenvalues

22 Matrix exponent. Equal eigenvalues 22. Matrix exponent Consider a first order differential equation of the form y = ay, a R, with the initial condition y) = y. Of course, we know that the solution to

### Principles of Modeling: Real World - Model World

MODELING BASICS Principles of Modeling: Real World - Model World Tony Starfield recorded: 2005 Welcome Welcome to Principles of Modeling We all build models on a daily basis. Sometimes we build them deliberately,

### YOU WILL NOT BE EFFECTIVE READING THIS.

This is the most effective and powerful script for securing appointment with FSBO's you will ever put to use. This scrip will increase your appointment closing ratio by 50-60%. The thing to keep in mind

### Telephone conversation between President Kennedy and Governor Ross Barnett September 29, 1962, 2:00 P.M.

Telephone conversation between President Kennedy and Governor Ross Barnett September 29, 1962, 2:00 P.M. President Kennedy: Hello? Hello, Governor? Governor Barnett: All right. Yes. JFK: How are you? RB:

### Andrew: And then you went and you did an internship that turned everything around, right?

Andrew: This session is about profitable ad buying. It is led by Justin Brook. He is the founder of I Am Scalable, a digital ad agency that specializes in supplement companies, software companies and info

### Pre-Calculus Review Problems Solutions

MATH 1110 (Lecture 00) August 0, 01 1 Algebra and Geometry Pre-Calculus Review Problems Solutions Problem 1. Give equations for the following lines in both point-slope and slope-intercept form. (a) The

### Permission-Based Marketing for Lawyers

Permission-Based Marketing for Lawyers Jim Hart is a divorce attorney in Cary, North Carolina. Previously, his law practice was based in Florida. He owns several websites. Jameshartlaw.com redirects to

### Date. Hello, Good Afternoon and Welcome to Pegasus Racing! I cordially invite you to join me...

"I m One Of The UK s Top Horse Racing Tipsters & I m Going To Show You My Closely Guarded Secrets Of How I Make Thousands From Horse Racing So You Can Too!" Date Hello, Good Afternoon and Welcome to Pegasus

### Nonparametric Tests. Chi-Square Test for Independence

DDBA 8438: Nonparametric Statistics: The Chi-Square Test Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Nonparametric Statistics: The Chi-Square Test." My name is Dr. Jennifer Ann Morrow. In

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### PRE-TOURNAMENT INTERVIEW TRANSCRIPT: Tuesday, January 27, 2015

PRE-TOURNAMENT INTERVIEW TRANSCRIPT: Tuesday, January 27, 2015 LYDIA KO MODERATOR: Happy to be joined in the media center by Rolex Rankings No. 2, Lydia Ko. Lydia, you're coming off winning the CME last

### Quick Tricks for Multiplication

Quick Tricks for Multiplication Why multiply? A computer can multiply thousands of numbers in less than a second. A human is lucky to multiply two numbers in less than a minute. So we tend to have computers

### Series Convergence Tests Math 122 Calculus III D Joyce, Fall 2012

Some series converge, some diverge. Series Convergence Tests Math 22 Calculus III D Joyce, Fall 202 Geometric series. We ve already looked at these. We know when a geometric series converges and what it

### Calculus Vocabulary without the Technical Mumbo Jumbo

Calculus Vocabulary without the Technical Mumbo Jumbo Limits and Continuity By: Markis Gardner Table of Contents Average Rate of Change... 4 Average Speed... 5 Connected Graph... 6 Continuity at a point...

### Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Section 9 Order of Operations

Supplemental Worksheet Problems To Accompany: The Pre-Algebra Tutor: Volume 1 Please watch Section 9 of this DVD before working these problems. The DVD is located at: http://www.mathtutordvd.com/products/item66.cfm

### Note: Please use the actual date you accessed this material in your citation.

MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science, Fall 2005 Please use the following citation format: Sylvia Ceyer and Catherine Drennan, 5.111 Principles of Chemical Science,

### There is so much information out there about internet safety and you should definitely read up on that, but that's not what I want to talk about.

From the Blog Life As of Late by Sarah Brooks Parents: A Word about Instagram To the parents of middle-schoolers on Instagram: There is so much information out there about internet safety and you should

### Independent samples t-test. Dr. Tom Pierce Radford University

Independent samples t-test Dr. Tom Pierce Radford University The logic behind drawing causal conclusions from experiments The sampling distribution of the difference between means The standard error of

### MS Learn Online Feature Presentation Managing Symptoms: Vision Nancy Holland, Ed.D, RN, MSCN. Tom>> Welcome to MS Learn Online, I m Tom Kimball

Page 1 MS Learn Online Feature Presentation Managing Symptoms: Vision Nancy Holland, Ed.D, RN, MSCN Tom>> Welcome to MS Learn Online, I m Tom Kimball Tracey>> And I m Tracey Kimball. People living with

### Grade 6 Math Circles. Exponents

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles November 4/5, 2014 Exponents Quick Warm-up Evaluate the following: 1. 4 + 4 + 4 +

### 2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2

### CLASSROOM ENGLISH PHRASES

1. Good morning CLASSROOM ENGLISH PHRASES 2. How are you? Good morning, everybody. Good afternoon, everybody. Hello, everyone. Hello there, James. 3. Introductions My name is Mr/Mrs/Ms Kim. I'm your new

### Definition of Vertical Asymptote The line x = a is called a vertical asymptote of f (x) if at least one of the following is true: f (x) =

Vertical Asymptotes Definition of Vertical Asymptote The line x = a is called a vertical asymptote of f (x) if at least one of the following is true: lim f (x) = x a lim f (x) = lim x a lim f (x) = x a

### 4.4 Concavity and Curve Sketching

Concavity and Curve Sketching Section Notes Page We can use the second derivative to tell us if a graph is concave up or concave down To see if something is concave down or concave up we need to look at

### Introduction to Open Atrium s workflow

Okay welcome everybody! Thanks for attending the webinar today, my name is Mike Potter and we're going to be doing a demonstration today of some really exciting new features in open atrium 2 for handling

### The OkCupid Diaries. Holly White. I 'm sorry I never replied to this. It was too long. But you seem nice and have a nice face.

The OkCupid Diaries Completed between January 31 st and February 19 th 2013 Holly White I'm sorry I didn't reply to this, I'm not sure if I replied to the other two you're referring to, I think I did but

### BBC LEARNING ENGLISH 6 Minute English The Proms

BBC LEARNING ENGLISH 6 Minute English The Proms This is not a word-for-word transcript Hello and welcome to 6 Minute English. I'm and I'm. Hello. Now,, are you doing anything interesting tonight? Well,

### BBC LEARNING ENGLISH 6 Minute English Do we read to show off?

BBC LEARNING ENGLISH 6 Minute English Do we read to show off? This is not a word-for-word transcript Hello and welcome to 6 Minute English. I'm and I'm. Sorry, wait a minute. I'm just finishing this book.

### Graphing Rational Functions

Graphing Rational Functions A rational function is defined here as a function that is equal to a ratio of two polynomials p(x)/q(x) such that the degree of q(x) is at least 1. Examples: is a rational function

### TRIGONOMETRY Compound & Double angle formulae

TRIGONOMETRY Compound & Double angle formulae In order to master this section you must first learn the formulae, even though they will be given to you on the matric formula sheet. We call these formulae

### How to Perform a Break-Even Analysis in a Retail Store A Step by Step Guide

How to Perform a Break-Even Analysis in a Retail Store A Step by Step Guide By BizMove Management Training Institute Other free books by BizMove that may interest you: Free starting a business books Free

### 2. Select Point B and rotate it by 15 degrees. A new Point B' appears. 3. Drag each of the three points in turn.

In this activity you will use Sketchpad s Iterate command (on the Transform menu) to produce a spiral design. You ll also learn how to use parameters, and how to create animation action buttons for parameters.

### AP Calculus BC. All students enrolling in AP Calculus BC should have successfully completed AP Calculus AB.

AP Calculus BC Course Description: Advanced Placement Calculus BC is primarily concerned with developing the students understanding of the concepts of calculus and providing experiences with its methods

### BBC LEARNING ENGLISH 6 Minute Grammar Question tags

BBC LEARNING ENGLISH 6 Minute Grammar Question tags This is not a word-for-word transcript Hello. Welcome to 6 Minute Grammar with me,. And me,. Hello. Today's programme is about question tags, isn't it?

### Lesson 42c: PV Diagrams

Lesson 42c: V Diagrams From the last section, you were probably wondering what happens when we do something like add heat to a sealed cylinder. This sounds like a pretty dangerous idea if you think back

### CAHSEE on Target UC Davis, School and University Partnerships

UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 006 Director Sarah R. Martinez,

### Hi, Joel here, and thanks for joining me again, I really appreciate it.

The Self-Publishing Blueprint by Joel Friedlander Hi, Joel here, and thanks for joining me again, I really appreciate it. Today we have the third video in this free training series, and I promised you

### Section 6-3 Double-Angle and Half-Angle Identities

6-3 Double-Angle and Half-Angle Identities 47 Section 6-3 Double-Angle and Half-Angle Identities Double-Angle Identities Half-Angle Identities This section develops another important set of identities

### Sequences and Series

Sequences and Series Consider the following sum: 2 + 4 + 8 + 6 + + 2 i + The dots at the end indicate that the sum goes on forever. Does this make sense? Can we assign a numerical value to an infinite

### GMAT SYLLABI. Types of Assignments - 1 -

GMAT SYLLABI The syllabi on the following pages list the math and verbal assignments for each class. Your homework assignments depend on your current math and verbal scores. Be sure to read How to Use

### Reach Your Target Audiences: Program Exposure and Gross Rating Points

Reach Your Target Audiences: Program Exposure and Gross Rating Points The following text emphasizes the importance of having an adequate exposure or reach of your marketing messages to influence health

### MATH 132: CALCULUS II SYLLABUS

MATH 32: CALCULUS II SYLLABUS Prerequisites: Successful completion of Math 3 (or its equivalent elsewhere). Math 27 is normally not a sufficient prerequisite for Math 32. Required Text: Calculus: Early

### FRANK BEAMER VIRGINIA TECH

FRANK BEAMER VIRGINIA TECH FRANK BEAMER: Well, we're getting ready to play a team that's in the same grouping as Ohio State, extremely talented, very wellcoached, look as hard as you can, you can't find