LIMIT OF A FUNCTION Meaning and
Definition
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The limit of a function is a fundamental concept in mathematics that describes the behavior of a function as its input approaches a certain value. In simpler terms, the limit of a function is the value that the function approaches as the input gets infinitely close to a given value, which may or may not be the same as the value of the function at that point.
Formally, if the function f(x) is defined for all x in a certain interval except possibly at a specific point c, then the limit of f(x) as x approaches c (written as lim(x→c) f(x), or just lim f(x)) is the value that f(x) gets arbitrarily close to as x gets arbitrarily close to c.
There are several scenarios that can arise when evaluating the limit of a function. The limit may exist and be finite, meaning that as x approaches c, f(x) has a well-defined and finite value. The limit may also be infinite, indicating that f(x) approaches positive or negative infinity as x approaches c. Alternatively, the limit may not exist, implying that as x approaches c, f(x) does not approach a single value or approaches different values depending on the direction from which x approaches c.
Understanding the limit of a function is essential for various mathematical applications and concepts, such as continuity, differentiation, and integration. It provides insights into how a function behaves around certain points and aids in the analysis of its properties and relationships.
