Hello, ilikedmath!
Divide top and bottom by
.
Divide top and bottom by
.
(1) ==
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. Would I then divide everything by what dominates the denominator? So "n" dominates the denominator so if I divide everything by n, I get: . I know that (1/n) goes to 0, but how can I get rid of the '3n'?
(2) =. Then I divided everything by 7^n since it dominates the denominator. I get: .
I can rewrite (4^n)/(7^n) as (4/7)^n. And since (4/7)^n goes to 0, the expression further simplifies to:
. But then if (4/7)^n goes to 0, I get 11/0 which is undefined. So I'm wrong.
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