- #1
benorin said:
No, if one is positive 1 and the other is negative 1, they are still different and thus the limit d.n.e. So it's not continuous there.MissP.25_5 said:
benorin said:
The definition of continuity for a function is that the limit of the function as x approaches a value must be equal to the value of the function at that point. In other words, the function must have no breaks or gaps in its graph.
To check if a function is continuous at a certain point, you must evaluate the function at that point and then take the limit of the function as x approaches that point. If the limit and the value of the function at that point are equal, then the function is continuous at that point.
Yes, a function can be continuous but not differentiable. This means that the function has no breaks or gaps in its graph, but it has a sharp turn or corner at a certain point, making it non-differentiable at that point.
Yes, if the graph of a function is continuous, then the function itself is continuous. This is because the graph represents the behavior of the function and if there are no breaks or gaps in the graph, then the function must also have no breaks or gaps.
Yes, a function can be continuous at all points. This means that the function has no breaks or gaps in its graph and is continuous at every single point on its domain.
