Is a sufficient and unnecessary condition. Infinite quantities (including positive and negative infinity) must be unbounded, because the absolute value of the function value can be arbitrarily large. However, being unbounded at (a, b) does not guarantee that it will be infinite at x0, because it may be unbounded near other points in (a, b) (for example, it will be infinite), so the function may be bounded at x0 and even have a finite limit. Moreover, even if an unbounded function appears near x0, there is no guarantee that it will become infinite at that point. Because the function may oscillate, and in the process of oscillation, it will return to the equilibrium point from a certain distance (within a limited range). Typical examples are: f (x) = (1/x) * sin (1/x), and f(0)=0. This function is defined in (-1, 1), but the function oscillates continuously at x=0.

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