if lim f(x) = -4 and lim h(x) = 4, what is the value of lim f(x)h(x)? x→1 x→1 x→1

Answer:

-16

Explanation:

Step1: Recall limit - product rule

The limit - product rule states that if $\lim_{x\rightarrow a}f(x)$ and $\lim_{x\rightarrow a}h(x)$ exist, then $\lim_{x\rightarrow a}[f(x)h(x)]=\lim_{x\rightarrow a}f(x)\cdot\lim_{x\rightarrow a}h(x)$.

Step2: Substitute given values

We are given that $\lim_{x\rightarrow 1}f(x)=-4$ and $\lim_{x\rightarrow 1}h(x)=4$. Substituting these values into the limit - product rule formula, we get $\lim_{x\rightarrow 1}[f(x)h(x)]=\lim_{x\rightarrow 1}f(x)\cdot\lim_{x\rightarrow 1}h(x)=(-4)\times4=-16$.