Question

question 9
1/1 pt
the graph of $y=f(x)$ (solid) and $y=g(x)$ (dashed) is shown
find the following limits.
$\lim_{x \to 1^{-}} \frac{f(x)}{g(x)} =$
$ -\infty$
$0$
$\infty$
does not exist
$\int(x)$

Explanation:

Step1: Find $\lim_{x \to 1} f(x)$

From the graph, as $x$ approaches 1, $f(x)$ approaches $-5$.
$\lim_{x \to 1} f(x) = -5$

Step2: Find $\lim_{x \to 1} g(x)$

From the graph, as $x$ approaches 1, $g(x)$ approaches $0$.
$\lim_{x \to 1} g(x) = 0$

Step3: Evaluate the ratio limit

We analyze the sign: as $x$ approaches 1, $f(x)$ is negative and $g(x)$ approaches 0 from the positive side (since $g(x)$ is near 0 and positive around $x=1$). So $\frac{f(x)}{g(x)}$ approaches negative infinity.
$\lim_{x \to 1} \frac{f(x)}{g(x)} = -\infty$

Answer:

$-\infty$