\(\lim\limits_{x \to \ -1}f(x) = \frac 3{x + 1}\)
\(L.H.L. =\lim\limits_{h \to 0} (-1 - h) =\lim\limits_{h \to 0} \frac 3{-1-h + 1}\)
\(= \lim\limits_{h \to 0} \frac 3{-h}\)
\(= -\infty\)
\(R.H.L. = \lim\limits_{h \to 0} f(-1 + h) = \lim\limits_{h \to 0} \frac {3}{-1 + h + 1}\)
\(= \lim\limits_{h \to 0} \frac 3{h}\)
\(= \infty\)
\(L.H.L. \ne R.H.L.\)
\(\therefore \lim\limits_{x \to \ -1 } \frac 3{x+ 1} \) does not exist.
