About Limits, Download Notes 

What Is Limits?

In mathematics, limits refer to the concept of determining the behavior of a function as its input values approach a particular value or as they approach infinity or negative infinity. The limit of a function is a fundamental concept in calculus and is used to analyze the behavior of functions, study continuity, and define derivatives and integrals.

Formally, the limit of a function f(x) as x approaches a particular value c is denoted as:

lim(x→c) f(x)

This notation represents the value that f(x) approaches as x gets arbitrarily close to c. If the limit exists and is equal to a specific value L, it can be written as:

lim(x→c) f(x) = L

Limits can also be evaluated from the left side (approaching from values smaller than c) and from the right side (approaching from values greater than c) to account for possible different behaviors on either side of c.

Limits are crucial in analyzing the behavior of functions, determining continuity, and evaluating derivatives and integrals in calculus. They provide a foundation for understanding the fundamental concepts of calculus and mathematical analysis.

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Table of Content

1. Limit of a Function.

2. Fundamental Theorems on Limits.

3. Some Important Expansions.

4. Methods of Evaluation of Limits