In calculus, the concept of limits at infinity is of great importance. A limit at infinity is used to determine the behavior of a function as the input approaches positive or negative infinity. To find the limit at infinity, we consider the leading term of the function and examine its behavior as the input becomes infinitely large.

For example, let's take the function f(x) = 2x^2 + 3x - 1. As x approaches infinity, the term 2x^2 dominates the function, as it becomes significantly larger than the other terms. Hence, the limit at infinity for this function is positive infinity.

Similarly, if we have a function g(x) = 3x^3 - 4x^2 + 5x, as x goes to negative infinity, the term -4x^2 becomes the dominant term, and the limit at negative infinity is negative infinity.

Determining limits at infinity is crucial for understanding the long-term behavior of functions and identifying horizontal asymptotes.