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

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 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 precise definition of a limit. (This is calculus 2 stuff...)

anonymous · Answer

do you know the precise definition of $$\lim_{x\to a}f(x)=\infty$$ ?

anonymous · Answer

yeah, the one where its like $$f(x)>M$$whenever$$0<\left| x-a \right|<\delta$$
its in my book i just don't want to type out the whole definition...