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math7
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/
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.