1. The problem statement, all variables and given/known data Suppose that limit x-> a f(x)= infinity and limit x-> a g(x) = c, where c is a real number. Prove each statement. (a) lim x-> a [f(x) + g(x)] = infinity (b) lim x-> a [f(x)g(x)] = infinity if c > 0 (c) lim x-> a [f(x)g(x)] = negative infinity if c < 0 2. Relevant equations The limit laws would seem relevant, but the f(x) limit goes to infinity. 3. The attempt at a solution I'm completely lost on how to start this problem. How would I prove something like the limit laws using the precise definition of a limit when one of the limits don't exist?