When we're trying to figure out limits in calculus, one fun way to do it is by using a table of values. It’s like being a detective looking for clues to uncover the limit! Let’s break it down step by step.

Step-by-Step Guide

1. Pick a Function: First, choose a function you want to explore. For example, let’s use the function ( f(x) = \frac{x^2 - 1}{x - 1} ).

2. Select Values Near the Limit: Next, identify the point where you want to find the limit. Let’s say it's ( x = 1 ). Now, pick some numbers that are close to 1 from both sides, like 0.5, 0.9, 1.0, 1.1, and 1.5.

3. Calculate the Function Values: Now, plug these numbers into the function. Here’s what you get:

   • ( f(0.5) = \frac{0.5^2 - 1}{0.5 - 1} )
   • ( f(0.9) = \frac{0.9^2 - 1}{0.9 - 1} )
   • ( f(1.1) = \frac{1.1^2 - 1}{1.1 - 1} )
   • ( f(1.5) = \frac{1.5^2 - 1}{1.5 - 1} )

4. Look for Patterns: Next, write down these values in a table. As you get closer to 1, you should notice that the values of ( f(x) ) get closer to 2. This suggests that the limit is probably 2!

Conclusion

Using tables is a great way to help us see how functions behave. It allows us to easily understand what happens around the limit point. It’s like having a front-row seat to the action! Happy calculating!