Hi all,
Just wondering if any one can show some working out and explain the following problem:
lim x --> 0+ ( sqrt(x)*ln(x)) =
I know the answer is 0 and i guess you can say because 0* infinity = 0. However, i don't feel that is the correct working out. Could some one please show some working out as well as explaining it.
Thank you in advance,
ArTiCk
No! 0*infinity makes no sense!
now, are you in calculus. L'Hopital's rule seems pretty easy here *covers his ears to drown out the boos coming from the other mathematicians*
note that
this satisfies the conditions for using L'Hoptial's.
Apply L'Hopital's and we get
simplify this and take the limit
I have to do it...I dont know advanced you are, but if you have gotten to infinite series
and since is contained in this
as you can see every term will have an x in it, thus direct substitution will yield
EDIT: Also, are you aware of the conept of higher order infinitesimals with limits, ?
It is extremely pertinant as it is the key thing to proving the required result this way.
I do not know without doing a bit of reserch what would justify changing the limits in this case.
(or rather I do know what would justify changing the order of the limits, I just think that it would not be worth the effort of showing that it applied in this case, given that we have simpler methods available)
RonL