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MATH 221 { 1st SEMESTER CALCULUS LECTURE NOTES VERSION 2.0 (fall 2009) This is a self contained set of lecture notes for Math 221. The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. The LATEX and Python les
The Limit Laws. The limit of a sum is equal to the sum of the limits. The limit of a difference is equal to the difference of the limits. The limit of a constant times a function is equal to the constant times the limit of the function. The limit of a product is equal to the product of the limits.
• We will use limits to analyze asymptotic behaviors of functions and their graphs. • Limits will be formally defined near the end of the chapter. • Continuity of a function (at a point and on an interval) will be defined using limits.
INTRODUCTION TO CALCULUS Why do we worry about limits? One of the main reasons will is that we will soon de ne the derivative and integral using limits. A second reason is that limits of polynomials lead to function like the exponential function or logarithm function. An other reason is that one can use limits to de ne numbers like ˇ= 3: ...
Limits are a very powerful tool in mathematics and are used throughout calculus and beyond. The key idea is that a limit is what I like to call a \behavior operator". A limit will tell you the behavior of a function nearby a point.
Introduction to limits. Now that we’ve finished our lightning review of precalculus and functions, it’s time for our first really calculus-based notion: the limit. This is really a very intuitive concept, but it’s also kind of miraculous and lets us do some very powerful things.
Infinite Limit : We say lim f ( x ) = ¥ if we. x a. can make f ( x ) arbitrarily large (and positive) by taking x sufficiently close to a (on either side of a) without letting x = a . There is a similar definition for lim f. x a ( x ) = -¥. except we make f ( x ) arbitrarily large and negative.
