QuestionFind $\lim _{x \rightarrow 3} f(x)$ for the piecewise function $f(x)=\begin{cases} x^{2}-7 & x>3 \\ -4+2x & x<3 \end{cases}$.

Studdy Solution
Compare the left-hand limit and the right-hand limit.
$$\lim{x \rightarrow3^-} f(x) \neq \lim{x \rightarrow3^+} f(x)$$Since the left-hand limit and the right-hand limit are not equal, the limit of the function at $x =3$ does not exist.
So, $\lim{x \rightarrow3} f(x)$ = DNE