The limit to infinity refers to the behavior of a function as the input variable approaches infinity. It is a way to describe the end behavior of a function and determine its ultimate value.
To find the limit to infinity, you can evaluate the function at larger and larger values of the input variable. If the function approaches a specific value as the input variable gets larger and larger, then that value is the limit to infinity. Alternatively, you can use mathematical techniques such as L'Hopital's rule or algebraic manipulation to find the limit.
The purpose of finding the limit to infinity is to understand the behavior of a function at extremely large values. This can help in making predictions and decisions in various fields such as physics, economics, and engineering.
If the function approaches a specific value as the input variable gets larger and larger, then the limit to infinity exists and that value is the limit. However, if the function does not approach a specific value or approaches different values depending on the direction of the input variable, then the limit to infinity does not exist.
To solve for the limit to infinity in this equation, you can use algebraic manipulation to simplify the expression. In this case, you can factor out an x from the square root and then cancel it out with the x outside the square root. This leaves you with the limit of the square root of 1, which is equal to 1. Therefore, the limit to infinity of this equation is 1.