OpenStax is part of Rice University, which is a 501 (c) (3) nonprofit. Give today and help us reach more students. © 1999-2025, Rice University. Except where otherwise noted, textbooks on this site are …

In the previous section, we evaluated limits by looking at graphs or by constructing a table of values. In this section, we establish laws for calculating limits and learn how to apply these laws.

Limit Laws explained with color coded examples. All of the main laws in one place

Listed here are a couple of basic limits and the standard limit laws which, when used in conjunction, can find most limits. They are listed for standard, two-sided limits, but they work for all forms of limits. …

There are four fundamental limit operations in calculus. Let’s learn each limit operation with proof and examples to understand how to use them in mathematics. (1) l i m 𝑥 → 𝑎 (𝑓 (𝑥) + 𝑔 (𝑥)) = l i m 𝑥 → 𝑎 𝑓 (𝑥) + l i m 𝑥 …

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. …

Here’s the good news: We won’t have to identify ε and δ every time we want to find a limit. Limits have properties that we will use to make the process much more expedient.

Scroll down the page for more examples and solutions on how to use the Limit Laws. The laws of limits and how we use them to evaluate a limit. These laws are especially handy for continuous functions. …

Limit laws allow us to compute limits by breaking down complex expressions into simple pieces, and then evaluating the limit one piece at a time. These laws are really theorems that have been proven, …

Limit laws are important in manipulating and evaluating the limits of functions. Limit laws are helpful rules and properties we can use to evaluate a function’s limit. Limit laws are also helpful in …