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ozkan12
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for any upper semi continuous how we can take limit ? limit or limsup ? which one is true ?
ozkan12 said:for any upper semi continuous how we can take limit ? limit or limsup ? which one is true ?
A limit of upper semicontinuous function is a mathematical concept that describes the behavior of a function as the input values approach a certain point. It is defined as the maximum value that the function can take on at that point, or the supremum of all values of the function at points near the given point.
A limit of upper semicontinuous function is different from a limit of a continuous function in that it allows for the function to have jumps or gaps in its graph, whereas a continuous function must have a smooth and unbroken graph. Additionally, a limit of upper semicontinuous function may not exist at all points, while a limit of a continuous function always exists.
Limits of upper semicontinuous functions have various applications in fields such as economics, engineering, and physics. They can be used to analyze the stability of systems, optimize resource allocation, and model physical phenomena such as fluid flow and electrical circuits.
To determine the limit of an upper semicontinuous function, you first need to determine the behavior of the function at points near the given point. Then, you take the supremum of all values of the function at those points. This value is the limit of the function at the given point.
Yes, a limit of upper semicontinuous function can be infinity if the function has no upper bound at points near the given point. In this case, the supremum of all values of the function at those points would be infinity, and that would be the limit of the function at the given point.