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\documentclass[11pt]{article} \usepackage{amssymb,amsmath,graphicx} \begin{document} \newtheorem{theorem}{Theorem}[section] \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Ex. } \title{Basic Math} \author{Tim Flaherty} \date{\today} \maketitle \begin{abstract} In this lab we examine some of the basic math type-setting found in a typical Calculus text. \end{abstract} \section{Functions} We assume that students are familiar with the fundamentals regarding functions of a real variable. Concepts such as domain, range, evaluation, composition, and so on should be well understood. Also, students should be familiar with inverses of one-to-one functions. Various special functions, such as the trigonometric functions $\sin$, $\cos$, $\tan$, $\cot$, $\sec$, $\csc$, the exponential $\exp$, and logarithm $\log$ also need to be known. \subsection{Limits} The limit is necessary to define continuity, differentiation, and integration. Indeed, Calculus would not be possible without the study of limits. We have the definition of a limit. \begin{definition} We say that $\lim_{x\to a}=L$ if given any $\epsilon > 0$, there is a $\delta >0$ such that $|f(x)-L|<\epsilon$ whenever $0 < |x-a| <\delta$. \end{definition} \subsection{Continuity} A continuous function is one whose graph has no breaks" or jumps". Also, a continuous function is one in which small changes in the independent variable

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## This note was uploaded on 04/19/2011 for the course MATH 21126 taught by Professor Johnson during the Spring '11 term at Carnegie Mellon.

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