Limit Formula

What is a limit in calculus?

A limit in calculus describes the value that a function approaches as the input (or variable) approaches a certain point.

How do you evaluate a limit?

Limits can be evaluated using various methods, such as direct substitution, factoring, rationalizing, using special limit formulas, and applying the squeeze theorem or L’Hôpital’s rule.

What are some basic limit formulas?

Some basic limit formulas include:

What is the limit of a constant?

The limit of a constant k as x approaches any value is the constant itself i.e., lim_x→c​k = k.

What is the Squeeze Theorem?

The Squeeze Theorem states that if f(x) ≤ g(x) ≤ h(x) for all x near c (except possibly at c) and lim_x→c​f(x) = lim_x→ch(x) = L then

lim_x→cg(x) = L

Limits help us comprehend how functions behave as their inputs approach certain values. Think of a limit as the destination that a function aims to reach as the input gets closer and closer to a specific point.

In this article, we will explore the essential limit formulas that form the backbone of calculus. These formulas are like the rules of a game, guiding us on how to find limits in various scenarios. Whether you’re adding, subtracting, multiplying, or dividing functions, there are specific formulas to help you determine the limit.