Is this function continuous and differentiable?

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Homework Help Overview

The discussion revolves around the continuity and differentiability of a function, specifically examining the function f(x) = (x^2 - 1)/(x - 1). Participants are analyzing the implications of canceling terms in the function and the conditions under which it is defined.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the cancellation of the (x-1) term and its impact on continuity and differentiability. Questions arise regarding the function's behavior at x = 1 and the implications of undefined points. Some participants suggest using limits and l'Hôpital's rule to analyze the function further.

Discussion Status

The discussion is ongoing, with various interpretations of the function's properties being explored. Some participants express confusion over the definitions of continuity and differentiability, while others challenge the assumptions made about the function's domain. There is no explicit consensus on the correct answer, and multiple viewpoints are being considered.

Contextual Notes

There is a noted lack of clarity regarding the function's domain, with some participants arguing that the problem statement does not adequately specify it. This ambiguity contributes to the complexity of determining continuity and differentiability.

  • #31
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  • #32
Mes chers messieurs, there is no need for such a sophisticated debate, which most likely confuse the OP.

One commonly speaks of discontinuities if a point in a graph is missing, regardless of the domain. This is necessary to investigate the various types of singularities. Whether this is correct in a strict logical sense, as a non defined location might as well be considered outside of consideration, is in the end completely meaningless and a matter for philosophers and maybe logicians, although I doubt the latter will be interested. It is the type of discussion which never ends and which won't lead anywhere, and it is the reason we canceled philosophy from the board.

So whoever feels right, let it be so. Thirty posts for such a simple question are definitely twenty-five too many.

Thread will remain closed.
 
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