How to Put Limits on Desmos Graphing Calculator

Limits are fundamental concepts in calculus that describe the behavior of functions as inputs approach particular values. The Desmos graphing calculator provides an intuitive way to visualize and compute limits. This guide will walk you through setting up and interpreting limits in Desmos.

Introduction

Limits are essential in calculus for understanding how functions behave at specific points, especially where they might be undefined. Desmos makes it easy to explore limits visually and numerically. This guide covers:

How to set up a limit in Desmos
Different types of limits
Interpreting limit results
Common pitfalls and how to avoid them

Note: While Desmos provides a powerful tool for visualizing limits, it's important to understand the mathematical concepts behind them. This guide focuses on the calculator functionality rather than the theoretical aspects of limits.

Basic Usage

Setting Up a Limit

Open the Desmos graphing calculator at desmos.com/calculator
In the left sidebar, click "Expressions" if it's not already open
Type your function in the input box (e.g., "y = (x² - 4)/(x - 2)")
To set a limit, type "limit" followed by your function and the point you want to approach (e.g., "limit (x² - 4)/(x - 2) as x approaches 2")
Press Enter to see the limit result

Interpreting Results

Desmos will display the limit value if it exists. If the limit doesn't exist, Desmos will indicate this. For example:

For "limit (x² - 4)/(x - 2) as x approaches 2", Desmos shows 4
For "limit 1/x as x approaches 0", Desmos shows "does not exist"

Example formula: limit (x² - 4)/(x - 2) as x approaches 2

Result: 4

Advanced Techniques

One-Sided Limits

To compute one-sided limits, use "limit from left" or "limit from right":

"limit from left 1/x as x approaches 0" → -∞
"limit from right 1/x as x approaches 0" → ∞

Infinite Limits

For limits approaching infinity, use "limit as x approaches ∞" or "limit as x approaches -∞":

"limit as x approaches ∞ 1/x" → 0
"limit as x approaches -∞ 1/x" → 0

Limits at Infinity

To find limits at infinity, use "limit as x approaches ∞" or "limit as x approaches -∞":

"limit as x approaches ∞ x²" → ∞
"limit as x approaches -∞ x²" → ∞

Types of Limits

Limit Type	Description	Desmos Syntax
Finite Limit	Approaches a finite number	limit f(x) as x approaches a
Infinite Limit	Approaches infinity	limit f(x) as x approaches ∞
One-Sided Limit	Approaches from left or right	limit from left f(x) as x approaches a

Troubleshooting

Common Issues

Syntax errors: Double-check your function and limit syntax
Undefined limits: The function may have a vertical asymptote
Incorrect results: Verify your function and limit point

Verification Tips

Graph the function to visualize the behavior
Try different approaches to the same point
Check for discontinuities in the function

FAQ

Can I compute limits of multivariable functions in Desmos?: Currently, Desmos primarily supports limits of single-variable functions. For multivariable limits, you might need other tools.
How accurate are the limit calculations in Desmos?: Desmos uses numerical methods to approximate limits. For exact results, you may need symbolic computation software.
Can I compute limits of piecewise functions in Desmos?: Yes, you can define piecewise functions and compute their limits in Desmos.
Why does Desmos say my limit doesn't exist?: This typically indicates the function has a vertical asymptote or oscillates infinitely at that point.
How can I learn more about limits?: Check out resources from Khan Academy, Paul's Online Math Notes, or your calculus textbook.