MATH 137- Final Exam Guide - Comprehensive Notes for the exam ( 104 pages long!)

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MATH 137
Final EXAM
STUDY GUIDE
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University of Waterloo
MATH 137
Calculus I for Honours Mathematics
Fall 2017
Final Exam
Exam Guide
Part 2 of 2
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Table of Contents:
Part 2:
Review Chapters 1 -2
Chapter 1: Absolute Value Function
Chapter 1: Absolute Value Theorem: Measures distances
Chapter 1: Herons Algorithm
Chapter 1: Arithmetic Parts for Limits of Sequence
Chapter 1: Divergence and Monotone Convergence Theory
Chapter 1: Introduction to Series: A Geometric Series and the Divergence
Chapter 2: Limits and Continuity
Chapter 2: Limits and Continuity II
Chapter 2: Sequential Characterization of Limits
Chapter 2: Continuity I
Chapter 2: Continuity II
Chapter 2: Continuity and Intermediate Value Theorem
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Document Summary

Chapter 1: arithmetic parts for limits of sequence. Chapter 1: introduction to series: a geometric series and the divergence. |(cid:1876) 0| measure the distance of (cid:1876) from the origin. |(cid:1832) (cid:1833)| (cid:1877) (cid:1877) (cid:1876) (cid:1878) (cid:1876) (cid:1878) for < case for = case. Inequalities: triangle inequality i e. g. (cid:1832)((cid:1876)) is a height (cid:1833)((cid:1876)) is the height of a plane. Equality if (cid:1878) is between (cid:1876) and (cid:1877) or (cid:1878) =(cid:1876) or (cid:1876) =(cid:1877) |(cid:1854) (cid:1844)|(=)(cid:1876) ( ,(cid:1853) (cid:1854)) (cid:1876) ((cid:1853) +(cid:1854), ) (cid:1876) = 2 ( (cid:1876)(cid:2870) = 4. |(cid:1876) (cid:1853)| >(cid:1854) (cid:1876) = 2 => (cid:1876)(cid:2870) = 4. So, (cid:1876) = 2( ) (cid:1876)(cid:2870) = 4 (cid:1853)(cid:2869), (cid:1853)(cid:2870),(cid:1853)(cid:2871), . (cid:1853) (cid:1853) denotes a term. If we have a general formulae then we can write it. A sequence is an ordered list of numbers, in this course usually infinite. (cid:1853) (cid:1854) (cid:1853) (cid:1853) +(cid:1854)

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