Question

find the limit.
lim(x→ - 2) 1/(x + 2)
1/2
does not exist
-∞
∞

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 \(\lim_{x\to - 2^{-}}\frac{1}{x + 2}
eq\lim_{x\to - 2^{+}}\frac{1}{x + 2}\), the limit does not exist.

Answer:

Does not exist