Compute Limits Homework: a & b

[aid]

Homework Statement

Compute the limits:

a) \lim_{n \rightarrow \infty} n(2\sqrt{n^2 - n + 2} - 3\sqrt{n^2 + 1} + \sqrt{n^2 + 2n}),

b) \lim_{n \rightarrow \infty} n(n + 4\sqrt{n^2 + n} - 2\sqrt{n^2 - n} - 3\sqrt{n^2 + 2n}).

The Attempt at a Solution

Well, dividing by n^2 leads to nowhere as I still get \frac{0}{0}. I didn't figure out a good way to use squeeze theorem here neither. So, I'm stuck.

 

[tiny-tim]

hi aid!

yes, divide by n², then use an expansion for everything of the form √(1 + something)