One-sided limits are really important in calculus. They help us see how functions act as we get really close to a specific point, but from different directions. Here’s why they’re important:

• Understanding Behavior: Sometimes, a function can head towards different values when you look from the left side ($\lim_{x \to a^-} f(x)$) and the right side ($\lim_{x \to a^+} f(x)$). This can tell us if the limit is actually there!

• Helpful for Gaps or Jumps: If there’s a jump or a hole in the graph, one-sided limits help us figure out what’s going on near that spot.

• Useful in Real Life: When we look at real-world situations, like changes in speed or temperature, one-sided limits can show us what happens right before a big change.

• Building Block for Derivatives: Getting a handle on one-sided limits is important for understanding derivatives. This is especially true when we want to find the slope of a tangent line.

Overall, one-sided limits help give us a better idea of what’s happening around certain points on a graph!