What are the limits of the follwing sequences as n tends towards infinity?

(i) $\displaystyle \sqrt {{n}^{2}+1000}-n$

(ii) $\displaystyle \left( \left( n! \right) ^{{n}^{-2}} \right) ^{-1}$

(iii) $\displaystyle {\frac {{n}^{100}}{{ 1.001}^{n}}}$

(iv) $\displaystyle {\frac {n \left( 2\,n+3 \right) \left( 3\,n+4 \right) +2}{4\, \left(

n \left( 6\,n+7 \right) \right) ^{2}+5\,n \left( 6\,n+7 \right) +6}}$

I had a go at (iv) and got an answer 1/4....

Im not really sure how to do the others, they are part of a past exam paper and there is no mark scheme, so when i get to an answer im not sure if it is right or not!