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).

Thanks so much!!!!!!
I actually only need the proofs for a) and c)... if it helps, here's the link to the proof of a problem to (b): http://imageshack.us/photo/my-images/190/unledmkd.png/

Answer 1

A) When A is approaching a positive number it will approach Infinity Infinity + C = Infinity because Infinity + anything is infinity

B} When the constant C Is greater than 0 [ positive non zero number ] then multiplying it by any number in positive infinity will just make the limit reach POSITIVE infinity

C} Same thing as B But this time its less than 0 thus reaching negative infinity because

-C [ negative any number ] * Any number > 0 = Negative large number[ infinity ]

I hope this helps.