Are you ready to explore limits? Let's look at a cool way to understand them better—using tables! Tables can really help us figure out limits step by step.

What are Limits?

Limits show us what happens to a function as we get close to a certain point. They help answer this question: "What value does ( f(x) ) get nearer to when ( x ) gets close to a specific number?"

Using Tables to Evaluate Limits

Tables are a great way to see how a function acts near a certain number. Here’s how to use them:

1. Pick a Function: Let's choose the function ( f(x) = \frac{x^2 - 1}{x - 1} ).

2. Find the Limit Point: We're going to look at the limit as ( x ) gets close to 1, or ( \lim_{x \to 1} f(x) ).

3. Make a Table: Write down some x values that are close to 1 on both sides!

   • A little less than 1: 0.9, 0.99
   • Exactly at 1: 1
   • A little more than 1: 1.01, 1.1

   Here’s what your table could look like:

   | $x$ | $f(x)$ | |-------|-----------------| | 0.9 | 0.81 | | 0.99 | 0.9899 | | 1 | Undefined | | 1.01 | 1.0101 | | 1.1 | 1.21 |

4. Look at the Values: Notice how as ( x ) gets really close to 1, ( f(x) ) also gets close to 1!

Conclusion

Isn’t that cool? By using tables, we can easily see what value a function is getting closer to as the input approaches a certain number. This makes understanding limits much clearer and way more fun! Keep using this method, and soon you'll be a pro at limits!