# If there was a hole in the line at (2,3) and there is another point at (2,1), then would the graph be differentiable at that point and why?

If I understand the description correctly, the answer is no and the reason is below.

Longer answer

Since the derivative is the limit, the derivative also does not exist.

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No, the graph would not be differentiable at the point (2,3) if there is a hole at that point. Differentiability requires that the function is continuous and has a defined slope at the point in question. A hole indicates a discontinuity in the function, which means the function is not continuous at that point. Therefore, it would not be differentiable at the point (2,3).

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