Limits to positive infinity refer to the behavior of a function as its input approaches infinity from the positive side. It is used to determine the value that a function approaches, or "approaches as a limit", as its input grows without bound.
In mathematical notation, a limit to positive infinity is represented as lim f(x) = L, where x approaches positive infinity and L is the limit value that f(x) approaches.
While a limit to positive infinity deals with the behavior of a function as its input approaches infinity from the positive side, a limit to negative infinity deals with the behavior of a function as its input approaches infinity from the negative side.
A function can have a finite limit to positive infinity if its values approach a finite value as its input grows without bound. For example, the function f(x) = 1/x has a finite limit of 0 as x approaches positive infinity.
Studying limits to positive infinity allows us to understand the behavior of a function as its input grows without bound, which can help in analyzing and predicting the behavior of real-world phenomena. It is also a fundamental concept in calculus and is used to define derivatives and integrals.