A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It is used to determine the value that a function approaches or “approaches to” as the input gets closer and closer to a specified value.
To find the limit of a function, evaluate the function at values approaching the specified value from both the left and right sides. If the values approach the same number, that is the limit. If they approach different numbers, the limit does not exist.
Limits are important in calculus because they allow us to analyze the behavior of functions at specific points. They also help us to define continuity, derivatives, and integrals, which are key concepts in calculus.
Yes, a limit can approach infinity. This occurs when the input of a function approaches a value that causes the output to become infinitely large. In these cases, we say that the limit does not exist.
A one-sided limit only considers the values of a function as the input approaches a specified value from one direction (either the left or right). A two-sided limit takes into account both the left and right-hand side behavior of the function as the input approaches the specified value.