find the limit.\nlim(x→ - 2) 1/(x + 2)\n1/2\ndoes not exist\n-∞\n∞

Explanation:

Step1: Substitute x - value

Substitute (x = - 2) into (\frac{1}{x + 2}). When (x=-2), the denominator (x + 2=-2 + 2=0).

Step2: Analyze one - sided limits

As (x\to - 2^{+}), (x+2\to0^{+}), and (\frac{1}{x + 2}\to+\infty). As (x\to - 2^{-}), (x + 2\to0^{-}), and (\frac{1}{x+2}\to-\infty). Since the left - hand limit (\lim_{x\to - 2^{-}}\frac{1}{x + 2}\neq\lim_{x\to - 2^{+}}\frac{1}{x + 2}), the limit does not exist.

Answer:

Does not exist