Question

**WILL FAN AND MEDAL TO ANYONE THAT CAN GIVE CORRECT PROOFS FOR ANY PART**
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

I need to prove it using the precise definition of a limit (i.e. no limit laws).