Calculus Volume1-Openstax.pdf

Volume 1 Calculus Volume 1 SENIOR CONTRIBUTING AUTHORS EDWIN JED HERMAN,UNIVERSITY OF WISCONSIN-STEVENS POINT GILBERT STRANG,MASSACHUSETTS INSTITUTE OF TECHNOLOGY OpenStax Rice University 6100 Main Street MS-375 Houston,Texas 77005 To learn more about OpenStax,visit https:/openstax.org.Individual print copies and bulk orders can be purchased through our website.2018 Rice University.Textbook content produced by OpenStax is licensed under a Creative Commons Attribution Non-Commercial ShareAlike 4.0 International License(CC BY-NC-SA 4.0).Under this license,any user of this textbook or the textbook contents herein can share,remix,and build upon the content for noncommercial purposes only.Any adaptations must be shared under the same type of license.In any case of sharing the original or adapted material,whether in whole or in part,the user must provide proper attribution as follows:-If you noncommercially redistribute this textbook in a digital format(including but not limited to PDF and HTML),then you must retain on every page the following attribution:“Download for free at https:/openstax.org/details/books/calculus-volume-1.”-If you noncommercially redistribute this textbook in a print format,then you must include on every physical page the following attribution:“Download for free at https:/openstax.org/details/books/calculus-volume-1.”-If you noncommercially redistribute part of this textbook,then you must retain in every digital format page view(including but not limited to PDF and HTML)and on every physical printed page the following attribution:“Download for free at https:/openstax.org/details/books/calculus-volume-1.”-If you use this textbook as a bibliographic reference,please include https:/openstax.org/details/books/calculus-volume-1 in your citation.For questions regarding this licensing,please contact supportopenstax.org.Trademarks The OpenStax name,OpenStax logo,OpenStax book covers,OpenStax CNX name,OpenStax CNX logo,OpenStax Tutor name,Openstax Tutor logo,Connexions name,Connexions logo,Rice University name,and Rice University logo are not subject to the license and may not be reproduced without the prior and express written consent of Rice University.PRINT BOOK ISBN-10 1-938168-02-X PRINT BOOK ISBN-13 978-1-938168-02-4 PDF VERSION ISBN-10 1-947172-13-1 PDF VERSION ISBN-13 978-1-947172-13-5 Revision Number C1-2016-003(03/18)-MJ Original Publication Year 2016 OPENSTAX OpenStax provides free,peer-reviewed,openly licensed textbooks for introductory college and Advanced Placement courses and low-cost,personalized courseware that helps students learn.A nonprofit ed tech initiative based at Rice University,were committed to helping students access the tools they need to complete their courses and meet their educational goals.RICE UNIVERSITY OpenStax,OpenStax CNX,and OpenStax Tutor are initiatives of Rice University.As a leading research university with a distinctive commitment to undergraduate education,Rice University aspires to path-breaking research,unsurpassed teaching,and contributions to the betterment of our world.It seeks to fulfill this mission by cultivating a diverse community of learning and discovery that produces leaders across the spectrum of human endeavor.FOUNDATION SUPPORT OpenStax is grateful for the tremendous support of our sponsors.Without their strong engagement,the goal of free access to high-quality textbooks would remain just a dream.Laura and John Arnold Foundation(LJAF)actively seeks opportunities to invest in organizations and thought leaders that have a sincere interest in implementing fundamental changes that not only yield immediate gains,but also repair broken systems for future generations.LJAF currently focuses its strategic investments on education,criminal justice,research integrity,and public accountability.The William and Flora Hewlett Foundation has been making grants since 1967 to help solve social and environmental problems at home and around the world.The Foundation concentrates its resources on activities in education,the environment,global development and population,performing arts,and philanthropy,and makes grants to support disadvantaged communities in the San Francisco Bay Area.Calvin K.Kazanjian was the founder and president of Peter Paul(Almond Joy),Inc.He firmly believed that the more people understood about basic economics the happier and more prosperous they would be.Accordingly,he established the Calvin K.Kazanjian Economics Foundation Inc,in 1949 as a philanthropic,nonpolitical educational organization to support efforts that enhanced economic understanding.Guided by the belief that every life has equal value,the Bill&Melinda Gates Foundation works to help all people lead healthy,productive lives.In developing countries,it focuses on improving peoples health with vaccines and other life-saving tools and giving them the chance to lift themselves out of hunger and extreme poverty.In the United States,it seeks to significantly improve education so tha