nd the limit. 7) $lim_{x\rightarrow - 2}\frac{1}{x + 2}$ a) $infty$
nd the limit. 7) $lim_{x\rightarrow - 2}\frac{1}{x + 2}$ a) $infty$
Answer
Explanation:
Step1: Analyze the denominator
As $x\rightarrow - 2$, the denominator $x + 2\rightarrow0$.
Step2: Determine the sign - behavior
When $x$ approaches $-2$ from the left side ($x\lt - 2$), $x + 2\lt0$ and $\frac{1}{x + 2}\rightarrow-\infty$. When $x$ approaches $-2$ from the right side ($x\gt - 2$), $x + 2\gt0$ and $\frac{1}{x + 2}\rightarrow\infty$. 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. $\infty$