What is infinity over infinity?

In mathematics, when dealing with limits, a fraction in which both the numerator and denominator approach infinity is often denoted as "infinity over infinity." This is known as an indeterminate form because it does not have a unique value and further analysis is required to determine the limit.

When faced with the limit of infinity over infinity, various mathematical techniques such as L'Hôpital's Rule, factoring, simplification, and trigonometric identities can be used to evaluate the limit and find a meaningful result.

The concept of infinity over infinity is fundamental in calculus and is often encountered when dealing with functions that grow without bound as their input approaches certain values. It represents a situation where the rate at which both the numerator and denominator increase is unbounded, and the behavior of the function at that point needs to be carefully examined.

Overall, infinity over infinity is a mathematical expression that requires careful analysis and appropriate techniques to determine the limit accurately.