Creating and understanding tables to find limits is a really helpful skill. I used it a lot when I was learning about limits in pre-calculus. Here’s how you can do it too:

1. Choose a Function: First, pick a function. For example, let's use ( f(x) = \frac{x^2 - 1}{x - 1} ). We want to find the limit as ( x ) gets closer to ( 1 ).

2. Set Up Your Table: Next, make a table with ( x ) values that get nearer to ( 1 ). You'll want some numbers that are just a bit less than ( 1 ) and some that are just a bit more than ( 1 ). Here’s what the table might look like:

   | ( x ) | ( f(x) ) | |----------|-------------| | 0.9 | 0.9 | | 0.99 | 0.99 | | 1.0 | N/A | | 1.01 | 1.01 | | 1.1 | 1.1 |

3. Evaluate the Function: Now, you will find the function values for each of these ( x ) numbers. Watch how the values change as ( x ) approaches ( 1 ) from both sides.

4. Interpret the Results: Finally, look at the values of ( f(x) ) as ( x ) gets closer to ( 1 ). You’ll see that as ( x ) gets nearer to ( 1 ) from both sides, the values are approaching ( 1 ). This means you can say:

   $\lim_{x \to 1} f(x) = 1$

Using tables helps to make things clearer. It really makes understanding limits a lot easier!