Question

functions g and f are graphed. find lim(x→ - 3)(g(x)f(x)). choose 1 answer:

Explanation:

Step1: Recall limit - product rule

$\lim_{x
ightarrow a}(g(x)f(x))=\lim_{x
ightarrow a}g(x)\cdot\lim_{x
ightarrow a}f(x)$

Step2: Find $\lim_{x

ightarrow - 3}g(x)$
As $x$ approaches $-3$ from both the left - hand side and the right - hand side, $g(x)$ approaches $-1$. So, $\lim_{x
ightarrow - 3}g(x)=-1$.

Step3: Find $\lim_{x

ightarrow - 3}f(x)$
As $x$ approaches $-3$ from both the left - hand side and the right - hand side, $f(x)$ approaches $0$. So, $\lim_{x
ightarrow - 3}f(x)=0$.

Step4: Calculate $\lim_{x

ightarrow - 3}(g(x)f(x))$
Using the product rule $\lim_{x
ightarrow - 3}(g(x)f(x))=\lim_{x
ightarrow - 3}g(x)\cdot\lim_{x
ightarrow - 3}f(x)=(-1)\times0 = 0$

Answer:

$0$