Question

find the limit.
lim(x→3 - ) 1/(x + 3)
0
-∞
∞
-1

Explanation:

Step1: Analyze the denominator as x approaches -3 from the left

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: Analyze the fraction

The function is $y = \frac{1}{x + 3}$. Substituting $x=-3 - h$ into the function, we get $y=\frac{1}{-h}$. As $h\to0$ and $h > 0$, $\frac{1}{-h}\to-\infty$.

Answer:

$-\infty$