Mastering Limits with Desmos: A Step-by-Step Guide to Graphing Limits

How to Put Lim in Desmos: A Comprehensive Guide


Hello and welcome to this comprehensive guide on how to put lim in Desmos. Desmos is a powerful online graphing calculator that can handle complex mathematical functions and equations. Understanding how to use the “lim” function in Desmos can greatly enhance your mathematical analysis and problem-solving capabilities. In this article, we will explore the steps to effectively utilize the “lim” function in Desmos and discuss its strengths and weaknesses.

Understanding the “lim” Function

Before diving into the technicalities, let’s briefly explain what the “lim” function represents. In mathematics, “lim” stands for limit and is used to describe the behavior of a function as it approaches a certain value or infinity. It allows us to analyze the values of a function and determine its behavior in various scenarios.

Step 1: Accessing Desmos

To begin, open your web browser and navigate to the Desmos website. If you don’t have an account already, sign up for free to access all the features and functions of Desmos.

Step 2: Creating a Graph

Once you’ve logged in, you’ll be directed to the Desmos graphing calculator. Click on the “+” button to create a new graph. You can also open an existing graph or explore the gallery for pre-made graphs.

Step 3: Adding an Equation

Now, let’s add an equation to the graph. In the input bar at the top of the screen, type your desired equation. For example, if you want to find the limit of f(x) as x approaches a certain value, you can type “f(x)=(equation)”.

Step 4: Defining the Limit

To specify the limit, use the “lim” function followed by the variable and the value it approaches. For instance, if you want to find the limit of f(x) as x approaches 0, you can write “lim(f(x), x, 0)”.

Step 5: Analyzing the Result

Once you’ve entered the equation and defined the limit, press Enter or click the checkmark icon. Desmos will display the result of the limit calculation on the graph. You can further analyze the behavior of the function by zooming in or out, adjusting the window settings, or adding more equations.

Step 6: Exploring Limit Properties

Desmos allows you to investigate various properties of limits, such as one-sided limits, infinite limits, and limits at infinity. By modifying the equation and the value it approaches, you can explore different scenarios and observe the corresponding limit values.

Step 7: Saving and Sharing

Once you’re satisfied with your analysis, you can save the graph by clicking on the floppy disk icon. Desmos provides options to share the graph via a link, embed it on websites, or download it as an image for future reference.

Strengths of Using Desmos for Limits

Desmos offers several advantages when it comes to working with limits:

1. Visual Representation:

Desmos provides a visually intuitive representation of functions and their limits. The graphs allow you to observe the behavior of a function as it approaches a specific value, helping you grasp the concept more effectively.

2. Instant Feedback:

As you modify the equation or the limit value, Desmos recalculates and updates the graph in real-time. This instant feedback enables you to experiment and gain a deeper understanding of limit concepts.

3. Interactive Exploration:

Desmos allows you to interact with the graphs by zooming in, panning, and adjusting the viewing window. This interactivity enables you to analyze the behavior of functions more comprehensively and discover patterns or anomalies.

4. Wide Range of Functions:

Desmos supports a wide range of mathematical functions and expressions, allowing you to explore limits in various contexts. Whether you’re dealing with algebraic, trigonometric, exponential, or logarithmic functions, Desmos has you covered.

5. User-Friendly Interface:

The user-friendly interface of Desmos makes it accessible to both beginners and experienced users. The intuitive design and simple navigation ensure a smooth and hassle-free experience while working with limits.

6. Collaboration and Sharing:

Desmos allows you to collaborate with others by sharing graphs and working on them simultaneously. This feature fosters teamwork and enables efficient knowledge exchange among students, teachers, and researchers.

7. Free and Online:

One of the greatest strengths of Desmos is that it is completely free to use and accessible online. You can access the platform from any device with an internet connection, eliminating the need for expensive software or physical calculators.

Weaknesses of Using Desmos for Limits

While Desmos offers numerous benefits, it also has a few limitations when it comes to working with limits:

1. Simplistic Limit Notation:

Desmos uses a simplified notation for limits, which might not be suitable for advanced mathematical analysis. It lacks the rigor and formality required in certain academic or research settings.

2. Limited Symbolic Manipulation:

Desmos focuses primarily on graphical representations and numerical calculations. It lacks advanced symbolic manipulation capabilities, such as simplifying complex expressions or solving limit-related equations analytically.

3. Dependency on Internet:

Since Desmos is an online platform, it requires a stable internet connection to access and utilize its features. This dependency on the internet can be a limitation in certain situations, such as during exams or in areas with limited connectivity.

4. Complexity of Multi-Variable Limits:

While Desmos handles single-variable limits with ease, it might struggle with more complex multi-variable limits. Analyzing limits involving multiple variables or functions requires additional mathematical knowledge and techniques beyond the scope of Desmos.

5. Lack of Customization Options:

Desmos provides a range of customization options for graphs, but it might not fulfill the specific needs of every user. Advanced customization features, such as modifying the axes, labels, or gridlines, are limited in Desmos.

6. Potential Graphing Errors:

In rare cases, Desmos might encounter graphing errors when dealing with certain complex functions or limits. While these errors are infrequent, it’s important to double-check the results and verify their accuracy when working on critical projects.

7. Limited Offline Functionality:

Desmos is primarily an online tool, and its full functionality is only available when connected to the internet. Offline functionality is limited, and some features, such as sharing or saving graphs, might be inaccessible without an internet connection.

Frequently Asked Questions (FAQs)

1. Can Desmos calculate limits of trigonometric functions?

Yes, Desmos can handle limits of trigonometric functions. Simply input the desired trigonometric equation and specify the limit value to evaluate the limit.

2. Can Desmos calculate one-sided limits?

Yes, Desmos allows you to calculate both left-sided and right-sided limits. Modify the equation and define the limit accordingly to evaluate one-sided limits.

3. How accurate are the limit calculations in Desmos?

Desmos provides accurate limit calculations, but it’s always recommended to cross-verify the results using other mathematical tools or manual calculations for critical applications.

4. Can I use Desmos to find limits at infinity?

Yes, Desmos can calculate limits at infinity. Specify the variable and let it approach infinity to evaluate the corresponding limit.

5. Is Desmos suitable for advanced mathematical research?

While Desmos is a powerful tool, it might not fulfill all the requirements of advanced mathematical research. For complex or specialized analysis, dedicated mathematical software or programming languages may be more suitable.

6. Can Desmos handle limits involving logarithmic functions?

Yes, Desmos supports limits involving logarithmic functions. Input the logarithmic equation and define the limit value to evaluate the corresponding limit.

7. How can I share my Desmos graphs with others?

Desmos provides multiple sharing options. You can generate a shareable link, embed the graph on websites, or download it as an image to share with others.

8. Can Desmos calculate limits involving piecewise functions?

Yes, Desmos can handle limits involving piecewise functions. Simply define the function and the corresponding limit to evaluate the desired limit.

9. Is there a limit to the number of equations I can add to a graph in Desmos?

No, Desmos allows you to add multiple equations to a single graph. You can analyze the limits of each equation individually or study their interactions.

10. Can Desmos calculate limits of composite functions?

Yes, Desmos can calculate limits of composite functions. Input the composite function and specify the limit value to evaluate the limit.

11. Does Desmos support limits involving infinite discontinuities?

Yes, Desmos can handle limits involving infinite discontinuities. Input the equation and define the limit value to evaluate the limit at the infinite discontinuity.

12. Can Desmos handle limits involving exponential functions?

Yes, Desmos supports limits involving exponential functions. Input the exponential equation and define the limit value to evaluate the corresponding limit.

13. Is it possible to export Desmos graphs for offline use?

Desmos allows you to export graphs as images for offline use. Simply download the graph as an image and save it to your device for future reference.


In conclusion, understanding how to put lim in Desmos is an invaluable skill for anyone involved in mathematical analysis and problem-solving. Desmos offers a user-friendly and visually intuitive platform for exploring limits and gaining deeper insights into the behavior of functions. While it has certain limitations, its strengths outweigh the weaknesses, making it a valuable tool for students, teachers, and researchers alike. So, why wait? Start utilizing Desmos today and unlock the power of limits in your mathematical journey!

Closing Words and Disclaimer

Dear readers, we hope this comprehensive guide on how to put lim in Desmos has provided you with valuable insights and practical knowledge. While Desmos is a powerful tool, always remember to cross-verify the results and use critical thinking for accurate mathematical analysis. The information provided in this article is for educational purposes only and should not substitute professional advice. Happy graphing!

1Access the Desmos website
2Create a new graph
3Add an equation
4Define the limit using the “lim” function
5Analyze the result
6Explore limit properties
7Save and share the graph

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