[SOLVED] Help finding limits that approach ∞.

(1) http://www.cramster.com/Answer-Board...4375006159.gif=http://www.cramster.com/Answer-Board...4687501769.gif=http://www.cramster.com/Answer-Board...5312501522.gif

I rationalized the expression by multiplying the numerator and denominator by the conjugate of the denominator, but then I got stuck and didn't know where to go from there. It seems that my rationalizing just made finding the limit more complicated.(Thinking) Would I then divide everything by what dominates the denominator? So "n" dominates the denominator so if I divide everything by n, I get: http://www.cramster.com/Answer-Board...1875008028.gif. I know that (1/n) goes to 0, but how can I get rid of the '3n'?

(2) http://www.cramster.com/Answer-Board...0937509543.gif=http://www.cramster.com/Answer-Board...6875002188.gif. Then I divided everything by 7^n since it dominates the denominator. I get: http://www.cramster.com/Answer-Board...1875006148.gif.

I can rewrite (4^n)/(7^n) as (4/7)^n. And since (4/7)^n goes to 0, the expression further simplifies to:

http://www.cramster.com/Answer-Board...8125001062.gif. But then if (4/7)^n goes to 0, I get 11/0 which is undefined. So I'm wrong. (Headbang)

Do I need to use the squeeze theorem for these? I haven't had calculus in two years, so I am very rusty. This is for a intro to real analysis class.

Any help, tips, corrections, and/or suggestions are greatly appreciated.

Thank you for your time!

- Stumped Student(Nerd)