How Do Limits Behave for Piecewise Functions at Specific Points?

Thread starter nycmathguy
Start date Jun 17, 2021

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Homework Help Overview

The discussion revolves around the behavior of limits for a piecewise function at specific points, particularly focusing on limits as x approaches integers and rational numbers. Participants are investigating limits such as lim f(x) as x approaches 2 and 1/2, and exploring the implications of the function's definition.

Discussion Character

Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

Participants are attempting to understand the limits of the piecewise function by evaluating specific points and intervals. Questions are raised about the values of the function at integers versus non-integers, and the implications of continuity on limit behavior.

Discussion Status

The discussion is active, with participants offering various interpretations and questioning each other's reasoning. Some guidance has been provided regarding the distinction between function values and limit values, but there is no explicit consensus on the correct interpretations of the limits being discussed.

Contextual Notes

Participants have noted the need to show effort in their inquiries, as per forum rules, and there is a recognition that the problem may be challenging. The discussion includes references to previous threads and attempts to clarify misunderstandings regarding the function's behavior at specific points.

Jun 19, 2021

nycmathguy

Mark44 said:

So make sure you understand the difference between, say, ##f(c)## and ##\lim_{x \to c} f(x)##. For a continuous function f, they will be the same, but not necessarily so for discontinuous or piecewise-defined functions.

Will do.