Thread: how to find the bounds of this siquence..

(n^2+2)^0.5 - (n)^0.5

i thought of doing a limit where n->infinity

but here i get undefined form and even if i whould get some finite limite
it will only be one bound

and i cant do limit n->-infinity because its a sequence must be positive??

Originally Posted by transgalactic

(n^2+2)^0.5 - (n)^0.5

i thought of doing a limit where n->infinity

but here i get undefined form and even if i whould get some finite limite
it will only be one bound

and i cant do limit n->-infinity because its a sequence must be positive??

We have the sequence . To find the lower bound define . A little work shows that and the the second derivative is positive at that value, therefore it is an relative minimum. So now checking 0 the left-endpoint of the domain we find that is a lower bound. Now we can show that is unbounded above, the reason being that for every you can find a number such that . Also you can note that as n gets arbitrarily large that which clearly is unbounded above.

but its sequence "n" must be positive and whole
you cant input n=0.8
?

Originally Posted by transgalactic

but its sequence "n" must be positive and whole
you cant input n=0.8
?

I know that, but think about that if is a local min/ max then the values around it are closer (if continous) to it. So test the biggest integer after the number I gave you and the smallest before.