(Section 2.1: An Introduction to Limits) 2.1.21. FOOTNOTES1.Limits do not require continuity.In a later section, we will discuss continuity, a property of many functions that helps the lovers run along the graph of a function without having to jump or hop. In the first few problems of this section, we had the luxury of imagining the lovers running towards each other (one from the left, one from the right) while staying on the graph offand without having to jump or hop, provided they were placed on appropriate parts of the graph. Sometimes, the “run” really requires jumping or hopping. For example, consider the following functionf. It turns out to be true that limx±0fx()=0 . =0,ifxis a rational valuex,ifxis an irrational value±²³2.Misconceptions about limits.See “Why Is the Limit Concept So Difficult for Students?” by Sally Jacobs in the Fall 2002 edition (vol.24, No.1) of The AMATYC Review, pp.25-34.
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.