D. Limit of a Functions

he limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a.a. The concept of a limit is the fundamental concept of calculus and analysis. It is used to define the derivative and the definite integral, and it can also be used to analyze the local behavior of functions near points of interest.

Informally, a function is said to have a limit LL at aa if it is possible to make the function arbitrarily close to LL by choosing values closer and closer to aa. Note that the actual value at aa is irrelevant to the value of the limit.

The notation is as follows:

\lim_{x \to a} f(x) = L,

which is read as "the limit of f(x)f(x) as xx approaches aa is L.L."