Find limx→1 f(x) where f(x) = {( x^2 - 1, x ≤ 1) (-x^2 -1, x>1)

Question

Find lim_x→1 f(x) where f(x) =

\(\begin{cases} x^2-1, & x\leq1\\ -x^2-1, & x>1 \end{cases}\)

Answer 1

\(\lim\limits_{x \rightarrow 1^-}\) f(x) = \(\lim\limits_{x \rightarrow 1^-}\) (x²-1) = 0

\(\lim\limits_{x \rightarrow 1^+}\) f(x) = \(\lim\limits_{x \rightarrow 1^-}\) -x² = -2

Therefore; lim_x→1^- f(x) ≠ lim_x→1^-f(x) 

Hence lim_x→1^- f(x) does not exist.