FAQ
6. Answering Your Burning Questions
Q: What's the difference between right continuity and continuity?
A: Continuity requires both the right-hand limit and the left-hand limit to exist, be equal to each other, and be equal to the function's value at the point. Right continuity only cares about the right-hand limit. Think of continuity as a handshake that requires both hands to meet perfectly, while right continuity only requires one hand to reach the other.
Q: Can a function be right-continuous but not continuous?
A: Absolutely! As we discussed above, the function can be right-continuous, but the left-hand limit may not exist or may not be equal to the function's value. This leads to only a single side, or the right side, meeting the conditions for the function.
Q: How do I know which function to use when finding the right-hand limit if a function is defined piecewise?
A: When finding the right-hand limit (x a+), you only need to consider the part of the function definition that applies when x is slightly greater than 'a'. This means you would need to consider x+delta in the piecewise equation when looking at the right hand limit.
Q: Is right continuity the same as differentiability?
A: No, not at all. Differentiability is a much stronger condition. A function can be right-continuous without being differentiable. Think of a sharp corner. It can be right-continuous, but it doesn't have a well-defined derivative at the corner.
