Member warned about not including a solution effort
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
The limit laws would seem relevant, but the f(x) limit goes to infinity.
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?