Limit,

http://screencast.com/t/yFEkr1wbeM

Question

Limit,

http://screencast.com/t/yFEkr1wbeM

anonymous · Answer

So your question is how he can multiply infinite by infinite.... right?

anonymous · Answer

consider infinite to be a some very large number.and if u multiply dis large no. wid another large number...then i will also be much much greater dat we cant detect.

christos · Answer

That's right, my question is how he can claim a result of inf * inf when that is undefined

christos · Answer

inf * inf is like something/0  *UNDEFINED*

anonymous · Answer

Well same as what madrockz said but I think that he can do it but it just means that the end # you get will be undefined with it

christos · Answer

I really doubt this to be the case but thanks alot for the input ! Any further opinion would be welcome !

christos · Answer

@hartnn  Maybe you have any ideas ?

anonymous · Answer

Wait, what grade are you in...?

christos · Answer

university.

anonymous · Answer

That would explain why I dont know it. Lol

hartnn · Answer

i think the solution is incorrect

x^(-1/2) = 0 when x->infinity
so, denominator = 0*infinity = indeterminate

hartnn · Answer

and we need one more iteration of L h  rule 
2x^(1/2) / ln x ----> inf/inf form

hartnn · Answer

= 2 *(1/2) x^(-1/2) times x = x^(1/2)
and x^(1/2) when x->infinity = infinity = final answer

christos · Answer

hm hold on

hartnn · Answer

eh, but wolf shows final answer = 0 
i really can't make out where i made error....

christos · Answer

there is a tricky chain rule of ln(ln(x) that I think we missed there

christos · Answer

or no ?

hartnn · Answer

d/dx (ln ln x) = 1/ (x ln x)

christos · Answer

I go sort(x) ----> inf as well :O

hartnn · Answer

oh wait! sorry, that was x^(1/2) and not x^(-1/2)

christos · Answer

but if you differenciate it it will be minus

hartnn · Answer

why would u diff it ?

hartnn · Answer

as told earlier, in limits we consider inf*inf = inf

christos · Answer

soo that's not undefined ? It actually is inf * inf = inf ?

hartnn · Answer

only when x-> infinity 
without limits , its undefined

christos · Answer

inf * - inf = - inf ?

hartnn · Answer

seems madrocks was correct from the beginning...

yes

christos · Answer

but wait, how can I come to the final step in the first place ?

hartnn · Answer

what ?

christos · Answer

nothing nothinng I solved it ! The only thing that confused me was the inf * inf part, thanks !

christos · Answer

I would like to ask some additional questions if possible, what if the limit is ----> -inf ? Would I operate the same way ? Are there any other undefined functions that would be "defined" under a specific situation in limits ? @hartnn