# Homework Help: Theorem of continuity and limits converge

1. Nov 18, 2007

### Satyr

1. The problem statement, all variables and given/known data
If lim x--> a of [f(x) + g(x)]=2 and lim x--> a of [f(x) - g(x)] = 1, then find lim x--> a f(x)g(x)

2. Relevant equations
Theorems of continuity

3. The attempt at a solution
Since i'm not quite sure if what I began with was right, it didn't yield me any type of a valid answer. But from the theorems of continuity (lim x--> a of f(x)=f(a)), I began with saying lim x-->2 of [f(x)+g(x)]=2 and lim x-->1 of [f(x)-g(x)]=1

is that a good place to start? where do I go from here?
thanks

2. Nov 18, 2007

### Dick

You mean continuity of f and g tells you f(a)+g(a)=2 and f(a)-g(a)=1, right? That's two equations in two unknowns. You should be able to solve for f(a) and g(a).

3. Nov 18, 2007

### Satyr

right, i've figured that part
i was wondering where I begin doing that?

thanks

4. Nov 18, 2007

### Dick

Add the two equations together to get an equation for just f(a).