Find lim(x→1)f(x),where f(x)=

Question

Find :

 \(\lim\limits_{x \to 1}f(x),where\,f(x)= \begin{cases} x^2-1, & \quad \text n \leq{1}\\ -x^2-1, & \quad \text n>{ 1} \end{cases} \)

Answer 1

L.H.S

= \(\lim\limits_{x \to 1-}f(x)=\lim\limits_{x \to 1-}(x^2-1)\) 

= (1)²−1

= 1 − 1

= 0

And,

R.H.L

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

= −1² − 1

= −2 

Since  \(\lim\limits_{x \to 1+}f(x)≠\lim\limits_{x \to 1+}f(x),\)

So,  \(\lim\limits_{x \to 1}f(x) \) does not exists.