In order for a limit to exist, what must happen?
The values of f must tend to the same number L, as x approaches from either left or the rightYou can have one sided limits, but if they are not the same than that x value does not have a limit
In order for a limit to exist, the function must approach a specific value (finite or infinite) as the independent variable approaches a certain point. More formally, for a limit to exist at a certain point, the function must approach the same value from both the right and left sides of that point. This means that the limit must be approached in a consistent manner, regardless of the direction from which the independent variable approaches the point. If the function approaches different values from different directions, then the limit does not exist.
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Understanding Vertical Asymptotes in Mathematics: Definition, Examples, and SignificanceMastering Horizontal Asymptotes in Rational Functions: A Guide to the Three Essential Rules
Understanding Infinite Limits in Calculus: Exploring the Behavior of Functions Near Certain Points.
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