What Are Limits?

In mathematics, a limit is a particular value that a function or sequence approaches when the input or index of the function approaches a certain value. Put simply, limits are used to determine the behavior of a function as the input of the function approaches a certain value. This is particularly useful in calculus, which is a branch of mathematics that studies how a function changes as its input changes.

Why Are Finding Limits Graphically and Numerically Important?

The process of finding limits graphically and numerically is important because it can help students gain a better understanding of the behavior of a function. By graphing the function and then finding the limit, students can gain insight into how the function behaves when its input approaches a certain value. Additionally, by finding the limit numerically, students can gain a better understanding of how the function behaves as its input changes.

How Do You Find Limits Graphically and Numerically?

Finding limits graphically and numerically can be done by using a worksheet. On the worksheet, the student will be given a function to graph and then asked to find the limit by either graphing or numerically. To graph the function, the student will need to plot the points on the graph and then connect them with a line. To find the limit numerically, the student will need to use a numerical method such as the Newton-Raphson method or the Bisection method.

Tips for Finding Limits Graphically and Numerically

When finding limits graphically and numerically, there are a few tips that students should keep in mind. First, when graphing the function, students should make sure to plot all the points accurately. Second, when finding the limit numerically, students should use the method that is best suited to the problem at hand. Finally, students should always double check their work and make sure that the limit they have found is correct.

Conclusion

Finding limits graphically and numerically is an important part of high school math. By using a worksheet, students can gain a better understanding of how a function behaves as its input changes. Additionally, by using the tips outlined above, students can make sure that they are accurately finding the limits for their functions.