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.