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

Answer 1

\[\infty +c =\infty \] ?
infinity * -c = - infinity?

Answer 2

I do not know how to do it because you cannot use limit laws (because the first limit is not finite). I am supposed to prove it using the ε, δ definition of a limit.