Question

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).