Continuity is an important idea when we talk about limits in functions. Here’s why it matters:

• Smooth Sailing: When a function is continuous at a point, it means there are no sudden jumps or breaks. Think about driving on a smooth road. If the road is steady, you can easily guess where you’re going. That’s how limits work with continuous functions!

• Limit Equals Function Value: For a function to be continuous at a certain point (let's call it point $c$), the limit as you get close to $c$ from both sides must equal the function value at $c$. In simple math terms, this is $f(c) = \lim_{x \to c} f(x)$. This is really important because it shows how limits connect to the actual values of the function.

• Just Makes Sense: Continuity helps us easily understand how functions behave. If we reach a limit point and it’s continuous, we can feel sure about what will happen next.

In short, continuity helps us move through the world of limits easily. It’s a key part of our math journey!