functions g and h are graphed. find lim(x→ - 2)(g(x)h(x)). choose 1 answer:

Explanation:

Step1: Recall limit - product rule

$\lim_{x\rightarrow a}(f(x)g(x))=\lim_{x\rightarrow a}f(x)\cdot\lim_{x\rightarrow a}g(x)$ when both $\lim_{x\rightarrow a}f(x)$ and $\lim_{x\rightarrow a}g(x)$ exist.

Step2: Find $\lim_{x\rightarrow - 2}g(x)$

As $x$ approaches $-2$ from both the left - hand side and the right - hand side, $g(x)$ approaches $4$. So, $\lim_{x\rightarrow - 2}g(x)=4$.

Step3: Find $\lim_{x\rightarrow - 2}h(x)$

As $x$ approaches $-2$ from both the left - hand side and the right - hand side, $h(x)$ approaches $2$. So, $\lim_{x\rightarrow - 2}h(x)=2$.

Step4: Calculate $\lim_{x\rightarrow - 2}(g(x)h(x))$

Using the limit - product rule, $\lim_{x\rightarrow - 2}(g(x)h(x))=\lim_{x\rightarrow - 2}g(x)\cdot\lim_{x\rightarrow - 2}h(x)=4\times2 = 8$.

Answer:

$8$