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...)

Answer 1

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

Answer 2

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...