Using tables to find limits might seem easy, but it can actually be a bit tricky and frustrating for students. Here’s a simple step-by-step guide to help you understand this method better.

1. Find the Limit: First, figure out what limit you need to find. This is often written as $\lim_{x \to a} f(x)$. It might seem easy, but sometimes figuring out the exact value of $a$ can be tough, especially with harder functions.

2. Pick Values Near the Point: Next, choose some values of $x$ that are very close to $a$. This part can be hard—deciding how close is “close enough” can lead to mistakes. You should pick numbers on both sides of $a$. For example, you could use $a - 0.1$, $a - 0.01$, and then $a + 0.1$, $a + 0.01$.

3. Calculate Function Values: For each of the $x$ values you chose, calculate $f(x)$. It’s easy to make mistakes in these calculations, which can be frustrating. So, checking your work can help avoid these problems.

4. Look at the Results: Now, check the $f(x)$ values as $x$ gets closer to $a$. Many students find it hard to understand these numbers. It’s important to see if they go to a specific number or if they go off in different directions.

5. Wrap It Up: Based on what you see in your results, decide what the limit is. Sometimes, how you approach the limit might make you think of different answers, so careful checking is really important.

Even though this process can be tough, practicing and paying close attention can help you get better and find the right answers more consistently.