Question

functions h and f are graphed. find lim(x→1)(h(x)f(x)). choose 1 answer.

Explanation:

Step1: Recall limit - product rule

The limit of a product of two functions is the product of their limits, i.e., $\lim_{x
ightarrow a}(h(x)f(x))=\lim_{x
ightarrow a}h(x)\cdot\lim_{x
ightarrow a}f(x)$ if both $\lim_{x
ightarrow a}h(x)$ and $\lim_{x
ightarrow a}f(x)$ exist.

Step2: Find $\lim_{x

ightarrow1}h(x)$
Looking at the graph of $h(x)$, as $x$ approaches $1$ from both the left - hand side and the right - hand side, $h(x)$ approaches $4$. So, $\lim_{x
ightarrow1}h(x) = 4$.

Step3: Find $\lim_{x

ightarrow1}f(x)$
Looking at the graph of $f(x)$, as $x$ approaches $1$ from both the left - hand side and the right - hand side, $f(x)$ approaches $2$. So, $\lim_{x
ightarrow1}f(x)=2$.

Step4: Calculate $\lim_{x

ightarrow1}(h(x)f(x))$
Using the limit - product rule $\lim_{x
ightarrow1}(h(x)f(x))=\lim_{x
ightarrow1}h(x)\cdot\lim_{x
ightarrow1}f(x)=4\times2 = 8$.

Answer:

8