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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.
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.
limits everywhere. Rational functions like (x2 21)=(x + 1) have limits everywhere if the denominator has no roots. Functions like cos2(x)tan(x)=sin(x) can be healed by simpli cation. Prototype functions like sin(x)=xhave limits everywhere.
Bottom lines: The limit of a sum/difference/product is the sum/difference/product of the limits. For the most part, the limit of a quotient is the quotient of the limits, except when the limit of the denominator equals 0. Repeated application of Sum and Product Rules give us the limits of polynomial and rational functions (as long
Calculus: Limits and Asymptotes. Notes, examples, & practice quiz (with solutions) Topics include definitions, greatest integer function, strategies, infinity, slant asymptote, squeeze theorem, and more.
