I would not use the word "assuming" here- it is a fact.Jimmy25 said:So in this case, they are assuming that an infinite limit does not exist?
The limit of a function is the value that a function approaches as the input approaches a specific value. This value can be either a number or infinity.
The limit exists if the left-hand limit (approaching the value from the left) and the right-hand limit (approaching the value from the right) are equal. If they are not equal, the limit does not exist.
No, the limit cannot exist at a point where the function is undefined. This is because the function does not have a value at that point and therefore the limit cannot be determined.
There are several methods for evaluating limits, including direct substitution, factoring, and using algebraic manipulation. Other methods include using limits laws, L'Hopital's rule, and the squeeze theorem.
A function is continuous if the limit at a point exists and is equal to the function value at that point. Therefore, the existence of a limit is necessary for a function to be continuous. However, the existence of a limit does not always guarantee continuity.