Is this function continuous and differentiable?

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SUMMARY

The function f(x) = (x^2 - 1)/(x - 1) is not continuous or differentiable at x = 1 due to the undefined nature of f(1), which results in a 0/0 form. The cancellation of the (x-1) term leads to the simplified function f(x) = x + 1, which is continuous everywhere except at x = 1. The correct answer to the problem is C, as the function fails to meet the criteria for continuity and differentiability at that point.

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  • #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.

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