The concept of limit existence refers to the behavior of a function as its input approaches a certain value. It determines whether the function approaches a specific output value or diverges as the input value gets closer to the given value.
The value of a function at a specific point refers to the output of the function at that exact input value. On the other hand, limit existence considers the behavior of the function as the input approaches a given value, regardless of the actual output at that value.
A finite limit existence means that the function approaches a specific output value as the input approaches a given value. In other words, the function is continuously approaching a single value without any abrupt changes.
Yes, a function can have different limit existences at different points. This occurs when the function behaves differently as the input approaches different values. It is important to evaluate the limit existence at each point separately to fully understand the behavior of the function.
The limit existence of a function can be determined by evaluating the function at different input values that approach the given value. If the outputs approach a single value, then the limit existence is finite. If the outputs approach different values or diverge, then the limit existence does not exist.