Question

Let $y=f\left(x\right)$. What is the definition of $\underset{x\to c}{\lim }f\left(x\right)=L$?

Short answer

As such an $L$does not exist, we can say$\underset{x\to c}{\lim }f\left(x\right)$does not exist.

Step-by-step solution

Step 1. Given Information

$y=f\left(x\right)$is a function

We need to define$\underset{x\to c}{\lim }f\left(x\right)=L$

Step 2. Defining limx→cf(x)=L

The definition is as such
for $g>0$, there exists $\delta >0$such that $\left|f\right(x)-L|<\epsilon$whenever $x\in E$
(where $E\subseteq R$, the set of real numbers is R) and $0<|x-c|<\delta$
In this case, we can say that the limit of the function $f\left(x\right)$as $x$tends to $\text{'}c\text{'}$exists and it is $\text{'}L\text{'}$and we write it as

$\underset{x\to c}{\lim }f\left(x\right)=L$or$f\left(x\right)\to L$as$x\to c$