Finding Limit t->0: H'(r) and τ(r)

[urbanist]

Hi all,

If we have
$H'(r)=r+\tau(r)H(r)$

and

$\tau(r)=k+(H(r)/r)^a$

where

$a>0, k>0,$ and $H(0)=0$,

can we say anything about ${lim}_{r\rightarrow 0^+}\tau(r)$?

Thanks a lot!

 

[Simon Bridge]

Sure you can.
Note - the trouble with evaluating the limit just by putting r=0 is the 0/0 in the second term right?
So what role would the slope of H play in reconciling this problem?

 

[urbanist]

Yes, that fraction is the problem.

I tried to solve it with l'Hopital's rule, but just got into a recursion, as expected...