A limit is the value that a function comes close to as the input comes close to some value. When we use a function to solve a problem, sometimes certain values can not be used as inputs to the function, but we can see what the function comes close to when the input comes close to the value. Limits can be used to explain what happens in these cases.
Let \(f(x)\) be a function defined on an interval that contains \(x=a\), except possibly at \(x=a\). Then we say that,
\(\lim\limits_{x\to a}{f(x)=L}\), which reads "the limit of \(f\) of \(x\), as \(x\) approaches \(c\) equals \(L\)".
if for every number \(ε>0\) there is some number \(δ>0\) such that
\(|f(x)−L|<ε\) whenever \(0<|x−a|<δ\)
Limits are used to approximate values that a function or sequence approaches as the input approaches a certain value.
Limits are also used in many real-world applications, including engineering, physics, economics, and more. They help us understand how systems change over time and how functions behave as they approach a specific point.
Limits (mathematics) - Wikipedia
Calculus I - The Definition of the Limit
Calculus - The limit of a function from Youtube Channel: MySecretMathTutor