Question

functions h and f are graphed.
find $lim_{x
ightarrow - 1}(h(x)f(x))$.
choose 1 answer:

Explanation:

Step1: Recall limit - product rule

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

Step2: Find $\lim_{x

ightarrow - 1}h(x)$
As $x$ approaches $-1$ from both the left - hand side and the right - hand side of the graph of $y = h(x)$, $h(x)$ approaches $4$. So, $\lim_{x
ightarrow - 1}h(x)=4$.

Step3: Find $\lim_{x

ightarrow - 1}f(x)$
As $x$ approaches $-1$ from both the left - hand side and the right - hand side of the graph of $y = f(x)$, $f(x)$ approaches $4$. So, $\lim_{x
ightarrow - 1}f(x)=4$.

Step4: Calculate $\lim_{x

ightarrow - 1}(h(x)f(x))$
Using the product rule of limits, $\lim_{x
ightarrow - 1}(h(x)f(x))=\lim_{x
ightarrow - 1}h(x)\cdot\lim_{x
ightarrow - 1}f(x)=4\times4 = 16$.

Answer:

$16$