If lim f(x)=L then a is in the domain of f(x).
To understand the relationship between the limit of a function and the domain of the function, we need to consider the definition of limit
To understand the relationship between the limit of a function and the domain of the function, we need to consider the definition of limit.
The limit of a function, denoted as lim f(x) = L, represents the value that the function approaches as x gets arbitrarily close to a certain point. In other words, it represents the behavior of the function near a particular point.
Now, if a function has a limit at a certain point, it means that the function is defined and meaningful in the neighborhood of that point. In order for the limit to exist, it is essential that the function is defined at points arbitrarily close to the given point.
Hence, if lim f(x) = L, it implies that the function f(x) is defined and has a meaning in the vicinity of the point where the limit is evaluated. Thus, the point a must be within the domain of the function f(x).
In summary, if a function has a limit at a certain point, it implies that the value of a falls within the domain of the function.
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