# Activities to Teach Students to Find Limits Using Addition, Subtraction, and Multiplication Laws

As a math teacher, it is important to ensure that students have a strong understanding of limits, as this is a foundational concept required for more advanced mathematical concepts. In particular, understanding addition, subtraction, and multiplication laws can help students to find limits quickly and accurately. Here are some activities that can be used to teach students to find limits using these laws.

To teach students the addition law for limits, you can use a graph of a function with a limit that can be found through addition. For example, a graph of f(x) = x³ – 2x² + 5x – 3 can be used. Ask students to find the limit of the function as x approaches 2. To help them, give them some possible values of f(x) as x approaches 2, such as f(1.9), f(1.99), f(2.01), and f(2.1). Tell students to add these values to find the limit. After they add the values, they will notice that the result gets closer and closer to 2. Therefore, the limit of f(x) as x approaches 2 is 2.

2. Subtraction Law Activity:

For the subtraction law, you can use a similar approach as the addition law activity. However, instead of adding values, students will subtract them. For example, use a graph with a limit that can be found through subtraction. For example, a graph of f(x) = 1/x – 1/(x+1) can be used. Ask students to find the limit of the function as x approaches infinity. To help them, give them some possible values of f(x) as x approaches infinity, such as f(100), f(1,000), and f(10,000). Tell students to subtract these values to find the limit. They will notice that the result gets closer and closer to 1. Therefore, the limit of f(x) as x approaches infinity is 1.

3. Multiplication Law Activity:

To teach students the multiplication law for limits, use a graph with a limit that can be found through multiplication. For example, a graph of f(x) = (3x-2)/(x+1) can be used. Ask students to find the limit of the function as x approaches infinity. To help them, give them some possible values of f(x) as x approaches infinity, such as f(100), f(1,000), and f(10,000). Tell students to multiply these values to find the limit. They will notice that the result gets closer and closer to 3. Therefore, the limit of f(x) as x approaches infinity is 3.

Overall, these activities can help students to understand the addition, subtraction, and multiplication laws for finding limits. By using graphs and simple values, students can learn to apply these laws to more complex functions. With regular practice, these activities can help students to develop a strong understanding of limits and prepare them for more advanced math concepts.