Answer
$2$
Work Step by Step
Step 1. Identify the given conditions $\lim_{x\to c}(f(x)+g(x))=\lim_{x\to c}f(x)+\lim_{x\to c}g(x)=3$ and $\lim_{x\to c}(f(x)-g(x))=\lim_{x\to c}f(x)-\lim_{x\to c}g(x)=-1$
Step 2. Let $u=\lim_{x\to c}f(x)$ and $v=\lim_{x\to c}g(x)$, we have $\begin{cases} u+v=3 \\ u-v=-1 \end{cases}$
Step 3. Add up the above two equations to get $u=1$, which in turn gives $v=2$.
Step 4. Thus we have $\lim_{x\to c}f(x)g(x)=\lim_{x\to c}f(x)\lim_{x\to c}g(x)=uv=2$
