Question

When does a limit exist.

Answer 1

A limit exists in mathematics when the left-hand and right-hand limits of a function are equal and finite as the input approaches a certain value, indicating the function's behavior near that point.

Step-by-step explanation:

In mathematics, a limit exists when a function approaches a particular value as the input approaches some value. The concept of limits is fundamental to calculus and mathematical analysis and helps in understanding the behavior of functions as they get close to a specific point. To determine when a limit exists, one must consider if the left-hand limit (as x approaches the point from the left) and the right-hand limit (as x approaches from the right) are equal. If they are, and the value is finite, then the limit exists at that point. It's also important to note that if a function approaches the same value regardless of the path taken to reach that point, then the limit at that point exists.

Answer 2

In order for a limit to exist, the function has to approach a particular value. In the case shown above, the arrows on the function indicate that the the function becomes infinitely large. Since the function doesn't approach a particular value, the limit does not exist.

Step-by-step explanation: