Question

Find lim f(x), x->3- Can you please explain this. I dont know why but this is confusing me.

Answer 1

Function f(x) is a complex function, formed by 3 function. The limit while x -> 3- means that we take arguments which are on the left side of 3, so the function is going to achieve the value of 1, but there is a blank circle, so it cannot achieve it.

Answer 2

Hello,

$\lim_{x \to 3-} f(x)=1\ \ is\ since ( x\ \in\ Dom(f)\ and\ \forall\ \delta\ \textgreater\ 0 \ and$
$( x \in \ Dom( f ) \ and \ 3-\delta \ \le \ x \ \ \textless \ p ) == \textgreater \ 1 - \epsilon \ \le\ f ( x )\ \le \ 1 + \epsilon$

$\lim_{x \to 3+} f(x)=3$
$f(3)=7\\ \lim_{x \to 3} f(x) \ does\ not\ exist.$