What is a limit in maths? Explained in detail

Learn and know how to explain what is a limit in calculus. In calculus this is the first definition we are going to learn. Further concepts in calculus if you want to understand clearly, first know what is a limit exactly.

What is a limit in maths? Explained in detail

It is important that before knowing what is a limit? First we should know what is the Right Hand limit and what is the Left Hand Limit. So first we will discuss these two things and then we will discuss what is a limit. We will also discuss the conditions for existence of limit.

What is Right hand limit?

Let f(x) be a function, if this function f(x) approaches to M as “x” approaches to “a” from the right hand side, then we call “M” as the Right Hand Limit. Right Hand Limit in simple notation we will write it as R.H.L

What is Left hand limit?

Let f(x) be a function, if this function f(x) approaches to N as “x” approaches to “a” from the left hand side, then we call “N” as the Left Hand Limit. Left Hand Limit in simple notation we will write it as L.H.L

Check what is a limit?

Let f(x) be a function in “x”. Suppose if f(x) comes very close to K as “x” approaches to “a”, then we call “K” as the limit of the function f(x). We can express it as \lim _{ x\rightarrow a }{ f(x) } =k

What is a limit in maths? Explained in detail

Conditions for Existence of limit  as follows:

How to check that limit is exist or not for a given function at x=a.

If the values of left hand limit (L.H.L) and right hand limit (R.H.L) are equal then we say that limit exist otherwise limit doesn’t exists.

Note:

The value of a function f(x) at x= a and the limit of a function f(x) at x= a, sometimes values may be same but the meaning of these two things are different.

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