# What is the mathematical notion of limit and what role do Limits play in the study of functions?

**Notion of Limit**.

**Limits**can be thought of as a way to

**study**the tendency or trend of a

**function**as the input variable approaches a fixed value, or even as the input variable increases or decreases without bound.

Herein, what is the meaning of limit of a function?

In mathematics, a **limit** is the value that a **function** (or sequence) "approaches" as the input (or index) "approaches" some value. **Limits** are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.

Similarly, how do you find the limit of a function? Find the **limit** by rationalizing the numerator In this situation, if you multiply the numerator and denominator by the conjugate of the numerator, the term in the denominator that was a problem cancels out, and you'll be able to find the **limit**: Multiply the top and bottom of the fraction by the conjugate.

Likewise, how can the concept of a limit be used to understand the behavior of functions?

End **behavior** and the **concept** of **limit** Notice that as the values of x get larger and larger, the graph gets closer and closer to the x-axis. In terms of the **function** values, we **can** say that as x gets larger and larger, f(x) gets closer and closer to 0. Formally, this kind of **behavior** of a **function** is called a **limit**.

What is the purpose of limits in calculus?

A **limit** allows us to examine the tendency of a function around a given point even when the function is not defined at the point. Since its denominator is zero when x=1 , f(1) is undefined; however, its **limit** at x=1 exists and indicates that the function value approaches 2 there.