The Limit Notation, Single and Double Sided Limits

\definition["What is $y$ approaching when $x$ approaches $a$ from the right ($+$)?"]{Right Single-Sided Limit}{\(\lim_{x\to a^+} f(x)\)} \definition["What is $y$ approaching when $x$ approaches $a$ from the left ($-$)?"]{Left Single-Sided Limit}{\(\lim_{x\to a^-} f(x)\)} Watch! If both the left and right single-sided limit exists and is the same, the Double-Sided Limit exists.

\definition["What is \(y\) approaching when \(x\) approaches \(a\)?" This exists only if \(\lim_{x\to a^-} f(x)=\lim_{x\to a^+} f(x)\) ]{Left Single-Sided Limit}{\(\lim_{x\to a} f(x)\)} Vocab! When the Double-Sided Limit does not exist, it is called DOES NOT EXIST!. It is not! \(\cancel{undefined}\)