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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 essential point of calculus is to see this same pattern in “continuous time.” It’s not enough to look at the total or the change every hour or every minute. The distance and speed can be changing at every instant.
• 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.
Limits. Created by Tynan Lazarus. September 24, 2017. 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.
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.
• The existence of a limit of a function f as x approaches a(from one side or from both sidesdoes not depend on whether f is defined at a but only on whether f is ), defined for x near the number a.
