Consider the following limit:

lim (x^m-a^m)/(x^n-a^n), a is not = 0, m,n are positive integers

x-->a

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

(m(m-1)(m-2)....(3)(2)(1)x^(m-m)-m(m-1)(m-2)...(3)(2)(1)a^(m-m))

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(n(n-1)(n-2)...(3)(2)(1)x^(n-n)-n(n-1)(n-2)...(3)(2)(1)a^(n-n))

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.

Thanks