Question

nd the limit. 7) $lim_{x
ightarrow - 2}\frac{1}{x + 2}$ a) $infty$

Explanation:

Step1: Analyze the denominator

As $x
ightarrow - 2$, the denominator $x + 2
ightarrow0$.

Step2: Determine the sign - behavior

When $x$ approaches $-2$ from the left side ($x\lt - 2$), $x + 2\lt0$ and $\frac{1}{x + 2}
ightarrow-\infty$. When $x$ approaches $-2$ from the right side ($x\gt - 2$), $x + 2\gt0$ and $\frac{1}{x + 2}
ightarrow\infty$. Since the left - hand limit and the right - hand limit are not equal, the limit does not exist. In the context of one - sided infinite limits, we consider the general behavior as the function approaches infinity.

Answer:

A. $\infty$