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Ja4Coltrane
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Can anyone give me an example of a function f:[a,b]->R which is continuous almost everywhere yet unbounded?
Thanks!
Thanks!
An unbounded function is one that has no finite upper or lower limit. This means that as the input values approach infinity or negative infinity, the output values also approach infinity or negative infinity, respectively.
An unbounded function may still be continuous everywhere, meaning that it has no abrupt changes or breaks in its graph. However, a continuous everywhere function may still have a finite upper or lower limit, unlike an unbounded function.
Yes, it is possible for an unbounded function to be continuous at a specific point. This means that the function is defined and has a finite value at that point, and the limit of the function at that point also exists and is equal to the finite value.
Yes, an unbounded function can have a derivative. This means that the function is differentiable at a specific point, and its derivative exists at that point. However, the function may not be differentiable at all points due to its unbounded nature.
No, an unbounded function cannot have a definite integral. This is because the definite integral is used to find the area under the curve of a function, and an unbounded function has no finite upper or lower limit, making it impossible to calculate the area under the curve.