Question

Find $\lim_{x\rightarrow 1}$ f(x) where { x2 -1, x≤1 -x2-1, x>1

Answer 1

The given function is
f(x) ={ x2 -1, x≤1 -x2-1, x>1
$\lim_{x\rightarrow 1^-}$ f(x) =$\lim_{x\rightarrow 1}$ [x2 -1] = 12 -1 =1-1 = 0
$\lim_{x\rightarrow 1^+}$ f(x) = $\lim_{x\rightarrow 1}$ [-x2 -1] = -12 -1 =-1-1 = -2
It is observed that $\lim_{x\rightarrow 1^-}$ f(x) ≠$\lim_{x\rightarrow 1^+}$ f(x).
Hence , $\lim_{x\rightarrow 1}$ f(x) does not exist.