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How to solve this limit of greatest integer function (floor function)? These cookies help us tailor advertisements to better match your interests, manage the frequency with which you see an advertisement, and understand the effectiveness of our advertising. In interval x lying between -1/2 to +1/2, what will be the greatest integer of 1-x? In these cases, the greatest integer function, or a general step function, is likely used to model the situation. If you don't know how, you can find instructions. Uses for the greatest integer function can be found quite often in the world around us. - especially when it comes to billing and cost analysis. For instance, utility bills, such as gas, phone, or Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Here are some examples illustrating how to ask for discontinuities. WebThe greatest-integer function f(x) = has different right-hand and left-hand limits at each integer. Parenthetical Citation Concept & Example | What is a Parenthetical Citation? = () If you do not allow these cookies, some or all of the site features and services may not function properly. Sorted by: 4. Since lim(x) ()= () A function is a relationship between two variables so that each input has exactly one output. Learn more about Stack Overflow the company, and our products. Ed from the University of Pennsylvania where he currently works as an adjunct professor. Thanks. The greatest integer function is the function that takes any number as its input and creates the largest integer that is less than or equal to that value as its output. A discontinuity is a point at which a mathematical function is not continuous. Graphically, this can be seen on the coordinate plane: In particular, zooming in on each of these pieces reveals that the left endpoint exists, but the right endpoint does not: The right endpoint is not included in each step. Discover what is the greatest integer function and what is the greatest integer function equation. Case 1 : When x is not an integer