Question

functions f and h are graphed. find lim(x→0)(f(x)h(x)). choose 1 answer:

Explanation:

Step1: Recall limit - product rule

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

Step2: Find $\lim_{x

ightarrow0}f(x)$
From the graph of $f(x)$, as $x$ approaches 0 from both left and right, $\lim_{x
ightarrow0}f(x) = 0$.

Step3: Find $\lim_{x

ightarrow0}h(x)$
From the graph of $h(x)$, as $x$ approaches 0 from both left and right, $\lim_{x
ightarrow0}h(x)$ exists (let's say it is some finite value $L$).

Step4: Calculate $\lim_{x

ightarrow0}(f(x)h(x))$
$\lim_{x
ightarrow0}(f(x)h(x))=\lim_{x
ightarrow0}f(x)\cdot\lim_{x
ightarrow0}h(x)=0\times L = 0$.

Answer:

0