functions f and h are graphed. find lim(x→0)(f(x)h(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., $\lim_{x\rightarrow a}(f(x)h(x))=\lim_{x\rightarrow a}f(x)\cdot\lim_{x\rightarrow a}h(x)$ if both $\lim_{x\rightarrow a}f(x)$ and $\lim_{x\rightarrow a}h(x)$ exist.

Step2: Find $\lim_{x\rightarrow0}f(x)$

As $x$ approaches $0$ from both the left - hand side and the right - hand side, $f(x)$ approaches $1$. So, $\lim_{x\rightarrow0}f(x) = 1$.

Step3: Find $\lim_{x\rightarrow0}h(x)$

As $x$ approaches $0$ from both the left - hand side and the right - hand side, $h(x)$ approaches $0$. So, $\lim_{x\rightarrow0}h(x)=0$.

Step4: Calculate $\lim_{x\rightarrow0}(f(x)h(x))$

Using the limit - product rule $\lim_{x\rightarrow0}(f(x)h(x))=\lim_{x\rightarrow0}f(x)\cdot\lim_{x\rightarrow0}h(x)=1\times0 = 0$.

Answer:

$0$