Question

find the limit. lim(x→3 -) 1/(x + 3)

Explanation:

Step1: Analyze the denominator

As $x\to - 3^{-}$, we consider values of $x$ that are less than - 3. Let $x=-3 - h$, where $h>0$ and $h\to0$. Then $x + 3=-3 - h+3=-h$.

Step2: Substitute into the function

The function $\frac{1}{x + 3}$ becomes $\frac{1}{-h}$. As $h\to0$ and $h>0$, $\frac{1}{-h}\to-\infty$.

Answer:

$-\infty$