Limit from the left
In mathematics, the limit from the left refers to the behavior of a function or sequence as the input approaches a specific value from the left-hand side
In mathematics, the limit from the left refers to the behavior of a function or sequence as the input approaches a specific value from the left-hand side. It is denoted using the subscript “-“.
Formally, the limit from the left is defined as follows: Let f be a function defined on an open interval that contains a point c. If, for every number L, except possibly L itself, there exists a positive number δ such that |f(x) – L| < ε for all x in the domain of f, where 0 < |x - c| < δ, then we say that the limit of f as x approaches c from the left is L, denoted as lim(x->c-) f(x) = L.
Practically, to find the limit from the left, we consider the behavior of the function as x approaches the specific value from the left-hand side. We evaluate the function at values of x that are less than the given value, and observe the trend of the output. If the function is approaching a specific value L from the left-side as x gets closer and closer to the given value, then the limit from the left is L.
It is important to note that the limit from the left only considers the behavior of the function or sequence as x approaches the given value from the left-hand side. If the limit does not exist from the left, it means that the function approaches different values depending on which side we approach the given value.
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