One common mistake students make with one-sided limits is mixing up the left-hand and right-hand limits.

1. Mixing Up Notation: Students often confuse $\lim_{x \to a^-} f(x)$ (left-hand limit) with $\lim_{x \to a^+} f(x)$ (right-hand limit). This can lead to incorrect answers.

2. Not Checking Both Sides: Sometimes, students forget to look at how the function behaves on both sides of the limit. This is especially important for piecewise functions, which have different rules in different sections.

3. Thinking Continuity Means No Difference: Many students think that if a function is continuous, the left-hand and right-hand limits will always be the same. That’s not always the case!

If you keep these common mistakes in mind, it can really help you understand limits better!