Consider the following limit:
lim (x^m-a^m)/(x^n-a^n), a is not = 0, m,n are positive integers
this obviously gives us a 0/0 limit if we use direct substitution, hence I was told to use l'Hopital's rule to evaluate this limit.
However I ran into a little problem in that if i keep differentiating the top and the bottom, i'll just keep getting a limit in the indeterminate 0/0 form.
This carries on until the very end when i get
which is as far as i can see still an indeterminate form.
So am i right to suggest that this limit cannot be evaluated?
Any help would be welcome.