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Pages 2

Persuasive Essay—Heroes

A persuasive essay is a sound argument of a position backed up with facts, details, examples and one additional element—appeal. Persuasion is the kind of writing that depends on the reader’s reaction to what the writer says. One should remember that the goal of persuasive writing is to make the reader change from his viewpoint to the writer’s viewpoint. Therefore, the writer must present his argument in a way that will not offend his reader.

• TOPIC: In the epic poem Iliad, who best fits the traits of the hero? Hector or Achilles?

In your essay, persuade your audience that either Achilles or Hector is the better example of the archetypal hero.

I. Introduction • Begin your introductory paragraph by discussing the fact that heroes have many characteristics. • List some possible heroic characteristics. • Include the title of the epic and the author (Homer). • State your thesis at the end of the paragraph—Achilles or Hector is the better hero

II. Body Paragraphs • Begin each body paragraph with a topic sentence—an example of an archetypal/epic hero trait that the hero possesses • Include specific examples from the Iliad. • End each paragraph with a Clincher/Transition sentence that wraps up this idea and moves us to the next idea.

Warning **Pitfalls to avoid in body paragraphs: stereotypes, name-calling, slanting the truth, quoting out of context, and distortions of the oppositions’ views. Remember: Using unfair persuasive techniques to disguise weakness in one’s own position or to discredit the opposition’s views that are worthy of serious attention is propaganda.

V. Conclusion Paragraph • Begin the conclusion paragraph by introducing a new, but related idea. • Make a general statement about your hero choice and why he is the better hero • Make a general…...

...SOME DIFFERENTIAL CALCULUS YOU MAY NEED 1. THE FIRST DERIVATIVE 1.1 For a power function y = f(x) = Axm , dy/dx = Amxm-‐1 This holds for ALL values of m. If m= 0, i.e.-‐ y = Ax0 (which is equal to A) dy/dx = A0x0-‐1 = 0. So the derivative of a fixed (constant) quantity is zero Examples: a. For a linear function of a single variable: y = f(x) = ax dy/dx = a Thus for a cost function C(q) = 4q, the marginal cost dC/dq = 4 b. For an affine (linear with intercept) function: y = f(x) = c + mx dy/dx = m (note that the c vanishes) For a cost function with a fixed cost, C(q) = 180 + 3q, dC/dq = 3 c. We can also get a function of mixed higher order polynomials y = f(x) = a + bx + cx2+ dx3 dy/dx = b + 2cx + 3dx2 For a cost function C(q) = 150 + 34q3 + 20q2, ......

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...Justin Ladd Calc 1 4/12/2011 Mini Project 2 Mini Project 2 For this project I took a different approach. I wanted to try something that was a little more changeling for me and at the same time I wanted a problem that would make me think. I know for some people that this may not seem to be that hard of a problem but for me these types of problem are difficult. I wanted to pick a problem that pertained to my major, which is Mechanical Engineering but that did not work out to well for me on the last project because I ended up treating the problem like an engineering problem and not a calculus problem, so with that being said that’s one reason that I picked this problem. The other reason that I choose this problem is that it seemed interesting to me and it is a story problem. For me personally I struggle with story problems and have difficulty comprehending what the problem is asking me to find. So let me tell what the problem is and then I will explain how I think it is related to the curriculum and a real world phenomenon: A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min, how fast is the water level rising when the water is 30 cm deep? This problem is related to the curriculum because it is about linear approximation and differentials (Stewart). We covered this section is......

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...Section 1.2 (Page 87) (Calculus Book): 14, 23, 26, 29, 30, 31, and 32 14.��������→�� ���� +���� −����+�� ���� −����+�� ���� + ���� − ���� + �� = ������ �� ��→�� �� − ���� + ���� − �� − ���� + �� ���� − ���� + ������ − ���� − ���� + �� = ������ �� ��→�� �� �� − �� + �� �� − �� − �� �� − �� ���� �� − �� + ���� �� − �� − �� �� − �� = ������ ��→�� ���� + �� − �� �� − �� ���� �� − �� + ���� �� − �� − �� �� − �� = ������ ��→�� �� − �� �� − �� �� − �� ���� + ���� − �� = ������ ��→�� �� − �� �� − �� ���� + ���� − �� − �� = ������ �� ��→�� �� + ���� − �� − �� = ������ ��→�� �� �� + �� − �� �� + �� �� �� + �� − �� �� + �� �� + �� �� − �� �� + �� �� − �� �� + �� �� + �� �� = = �� + �� �� + �� �� ��+�� ���� −���� = ������ ��→�� = ������ ��→�� 23 ������ ��→�� = ������ ��+�� ��→�� ��+�� ��−�� ⟹ ������ ��→�� �� �� �� = = = ������������������ ∴ ���������� ����������′ �� ���������� �� − �� �� − �� �� ��−�� ���� −����−�� 26 ������ ��→�� = ������ ��→�� ��−�� ���� −����+����−�� = ������ ��−�� ��→�� �� ��−�� +�� ��−�� Page | 1 = ������ ��→�� �� − �� �� − �� −�� �� = = = �� − �� �� + �� �� − �� �� + �� �� × �� �� ∴ ���������� �������� ������ ����������. �� − �� ��−�� �� �� = ������������������; 29������ ��→�� ��−�� ��−�� = ������ ��→�� = ������ ��→�� ��−�� ��+�� ��−�� = ������ ��→�� �� + �� = �� + �� = �� + �� = �� ��−�� 30������ ��→�� ��− �� = ������ �� ��......

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...Project Gutenberg EBook of Calculus Made Easy, by Silvanus Thompson This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: Calculus Made Easy Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differentia Author: Silvanus Thompson Release Date: October 9, 2012 [EBook #33283] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK CALCULUS MADE EASY *** Produced by Andrew D. Hwang, Brenda Lewis and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) transcriber’s note Minor presentational changes, and minor typographical and numerical corrections, have been made without comment. All A textual changes are detailed in the L TEX source ﬁle. This PDF ﬁle is optimized for screen viewing, but may easily be A recompiled for printing. Please see the preamble of the L TEX source ﬁle for instructions. CALCULUS MADE EASY MACMILLAN AND CO., Limited LONDON : BOMBAY : CALCUTTA MELBOURNE THE MACMILLAN COMPANY NEW YORK : BOSTON : CHICAGO DALLAS : SAN FRANCISCO THE MACMILLAN CO. OF CANADA, Ltd. TORONTO CALCULUS MADE EASY: BEING A......

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...Preface Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus. I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an Algebra or Trig class or contained in other sections of the notes. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. 1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn calculus I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasn’t covered in class. 2. Because I want these notes to provide some more examples for you to read through, I don’t always work the same problems in class as those given in the notes. Likewise, even if I do work some of the problems in here I may work fewer problems in class than are presented here. 3. Sometimes questions in class will lead down paths that are not covered here. I try to anticipate as many of the questions as possible when writing these up, but the reality is that I can’t anticipate all the questions. Sometimes a very good......

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...from one extreme to the next in their lifetime making it impossible. However every circumstance provides practice which intern lands you one step closer to Eudemonia. Focusing on the agent himself rather than the act is in my opinion the most significant difference between Virtue Theory, Utilitarianism and Duty Theory. The Utilitarian only concerns himself with the effect of the action. They measure moral actions based on pleasures and pains. The Utilitarian must attempt to do what is best for the majority without considering what is best for him. In some instances the Utilitarian will list out all of the pleasures and pains of an action; using the Hedonistic calculus to measure if the action produces the greatest amount of pleasure for the majority. The Virtue theorist doesn’t acknowledge the Hedonistic Calculus; he only concerns himself with how he should act and how to find the medium between the deficiency and excessiveness of virtue. Example: Moral Dilemma: Is it morally wrong to break the speed limit in an effort to make it to the hospital to see your first child born. Pleasures/benefits He gets to see his first child born He will be there to hold his wife’s hand and offer her moral support during a difficult time. He will be able to share the story with his child and describe how he felt during that one in a life time experience. Pains/cons He could get a ticket Based on this the Utilitarian would say yes it is morally right to break the speed......

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...random measures on [0, ∞), relative to a given ﬁltered probability space Ω, F , (Ft )t≥0 , P , where (Ft ) is a right continuous ﬁltration of (F , P) complete sub-σ-ﬁelds of F . This theory was gradually created from results which originated from the study of Markov processes, and martingales and additive functionals associated with them. A guiding principle for Meyer and Dellacherie was to understand to which extent the Markov property could be avoided; in fact, they were able to get rid of the Markov property in a radical way. At this point, we would like to emphasize that, perhaps to the astonishment of some readers, stochastic calculus was not thought of as a basic “elementary” tool in 1972, when C. Dellacherie’s little book appeared. Thus it seemed interesting to view some important facts of the general theory in relation with stochastic calculus. The present essay falls into two parts: the ﬁrst part, consisting of sections 2 to 5, is a review of the General Theory of Stochastic Processes and is fairly well known. The second part is a review of more recent results, and is much less so. Throughout this essay we try to illustrate as much as possible the results with examples. More precisely, the plan of the essay is as follows: • in Section 2, we recall the basic notions of the theory: stopping times, the optional and predictable σ-ﬁelds and processes,etc. • in Section 3, we present the fundamental Section theorems; • in Section 4, we present the fundamental Projection......

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...Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of......

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...Tutorial 1 – Vector Calculus 1. Find the magnitude of the vector PQ with P (−1,2) and Q (5,5) . 2. Find the length of the vector v = 2,3,−7 . 3. Given the points in 3-dimensional space, P ( 2,1,5), Q (3,5,7), R (1,−3,−2) and S ( 2,1,0) . Does r PQ = RS ? ˆ ˆ 4. Find a vector of magnitude 5 in the direction of v = 3i + 5 ˆ − 2k . j r r ˆ ˆ ˆ j ˆ 5. Given u = 3i − ˆ − 6k and v = −i + 12k , find (a) u • v , r r (b) the angle between vectors u and v , r (c) the vector proju v , r r r r (d) the scalar component of v in the direction of u . 6. Given P (1,−1,3), Q ( 2,0,1) and R (0,2,−1) , find (a) the area of the triangle determined by the points P, Q and R. (b) the unit vector perpendicular to the plane PQR. 7. Find the volume of the parallelepiped determined by the vectors u = 4,1,0 , v = 2,−2,3 and r r r r r w = 0,2,5 . 8. Find the area of the parallelogram whose vertices are given by the points A (0, 0, 0), B (3, 2, 4), C (5, 1, 4) and D (2, -1, 0). ˆ j 9. Find the equation of the line through (2, 1, 0) and perpendicular to both i + ˆ and ˆ + k . j ˆ 10. Find the parametric equation of the line through the point (1, 0, 6) and perpendicular to the plane x+3y+z=5. 11. Determine whether the given lines are skew, parallel or intersecting. If the lines are intersecting, what is the angle between them? L1: x −1 y −3 z−2 = = 2 2 −1 x−2 y−6 z+3 L2 : = = 1 −1 3 12. Find the point in which the line x = 1 –t, y = 3t, z = 1 + t meets...

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...Calculus From Wikipedia, the free encyclopedia This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus [show]Integral calculus [show]Vector calculus [show]Multivariable calculus Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits,functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modernmathematics education. It has two major branches,differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient. Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional......

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...for my masters here at NMSU. In order to meet the prerequisites for the MBA program, I needed to take calculus and I’m glad I did because I wouldn’t have otherwise. Everything I learned in calculus challenged me to think critically and in another sense that I hadn’t known before. Being able to apply calculus to optimize a business’s performance, whether it be through current performance or future expectations is huge for any business. (Saiz, 2001) Since I can remember I’ve always felt like I am supposed to help my dad’s business despite it not really being my passion. I have found it to be difficult to work in that kind of environment. My dad’s business has done really well but it’s not something I love doing and honestly I don’t want anything given to me because of my dad’s successes, I want to do it on my own. The knowledge I have learned through college and the amount I have grown to be independent has made me realize that I can do anything. I have since decided to start my own in business in something I am extremely passionate about. Using calculus to determine rates to charge potential customer for optimal profits can really help my business get started. I think many people that start businesses jump into it without having structure and often times fail. I have found many tools and resources such as calculus to be very beneficial to the success of a business. Calculus will help my business predict maximum sales for a given service and help determine minimum costs......

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...Many gifted students such as myself accredit Gottfried Leibniz to be the precursor of their impending demise. Mr. Leibniz is the curator of Calculus, the idol of integrals, the devil of derivatives. Calculus is the study of change, and since it’s inception in the 17th century, it has changed the world. I also believe it to be the keystone to changing our future. Studies and general common sense show that our world is quickly deteriorating, and although judgements vary, it is no secret we will soon be evicted from Earth. Our future relies in physics, as it is our only foundation for understanding the world outside our world, and Calculus is our foundation for understanding our sole gateway. Physics would be just a game if it weren’t for Calculus, and we need the higher level of physics to comprehend what is outside our atmosphere and galaxy. Once the day approaches where humanity’s existence is futile and we are being shipped off to our new home in some foreign galaxy, Calculus will be our intellectual voucher to save humanity and all of it’s progression since our conception. Yes, I like all, have suffered through its limits and fundamental theorems, but I, unlike all, see the value in the deed. People love to hate it, but what I’ve learned while racing at the highest level, is that you need to embrace the struggle, and use that struggle to achieve something greater than yourself. I’ve lost entire days of my life studying for seemingly pointless tests, struggling to grasp......

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...Student Solutions Manual for SINGLE VARIABLE CALCULUS rS al e SEVENTH EDITION DANIEL ANDERSON University of Iowa Fo JEFFERY A. COLE Anoka-Ramsey Community College N ot DANIEL DRUCKER Wayne State University Australia . Brazil . Japan . Korea . Mexico . Singapore . Spain . United Kingdom . United States ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher except as may be permitted by the license terms below. For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, ISBN-13: 978-0-8400-4949-0 ISBN-10: 0-8400-4949-8 Brooks/Cole 20 Davis Drive Belmont, CA 94002-3098 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: www.cengage.com/global Cengage Learning products are represented in Canada by Nelson Education, Ltd. e © 2012 Brooks/Cole, Cengage......

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...Steven E. Shreve Stochastic Calculus for Finance I Student’s Manual: Solutions to Selected Exercises December 14, 2004 Springer Berlin Heidelberg NewYork Hong Kong London Milan Paris Tokyo Preface This document contains solutions to half the exercises appearing in Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer, 2003. Steven E. Shreve December 2004 Pittsburgh, Pennsylvania USA Contents 1 The Binomial No-Arbitrage Pricing Model . . . . . . . . . . . . . . . . 1.7 Solutions to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 7 7 2 Probability Theory on Coin Toss Space . . . . . . . . . . . . . . . . . . . . 2.9 Solutions to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 State Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.7 Solutions to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4 American Derivative Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.9 Solutions to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5 Random Walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.8 Solutions to Selected Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6 Interest-Rate-Dependent Assets . . . . . . . . . . . . . . . . . . . . . . ....

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...Kellie Aosley8 Recent Hedical school &a&ate "CALCULUS FOR THE UTTERLY CONFUSED has proven to be a wonderful review enabling me t o move forward in application of calculus and advanced topics in mathematics. I found it easy t o use and great as a reference for those darker aspects of calculus. I' Aaron Ladeville, Ekyiheeriky Student 'I1am so thankful for CALCULUS FOR THE UTTERLY CONFUSED! I started out Clueless but ended with an All' Erika Dickstein8 0usihess school Student "As a non-traditional student one thing I have learned is the Especially in importance of material supplementary t o texts. calculus it helps to have a second source, especially one as lucid and fun t o read as CALCULUS FOR THE UTTERtY CONFUSED. Anyone, whether you are a math weenie or not, will get something out of this book. With this book, your chances of survival in the calculus jungle are greatly increased.'I Brad &3~ker, Physics Student Other books i the Utterly Conhrsed Series include: n Financial Planning for the Utterly Confrcsed, Fifth Edition Job Hunting for the Utterly Confrcred Physics for the Utterly Confrred CALCULUS FOR THE UTTERLY CONFUSED Robert M. Oman Daniel M. Oman McGraw-Hill New York San Francisco Washington, D.C. Auckland Bogoth Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto Library of Congress Cataloging-in-Publication Data Oman, Robert M. Calculus for the utterly confused / Robert M.......

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