What is the Unknown Limit Theorem and How Can It Help with Limit Problems?

midododo11 · Feb 21, 2012

Has anybody heard of this theorem before? because it's in my school book and it works with most limit problems but I can't find its name or even find it in any reference book

$gif.latex?\lim_{x\rightarrow%20a}%20\frac{x^m-a^m}{x^n-a^n}=\frac{m}{n}\times%20a^{m-n}.gif$

Any help or guidance would be appreciated, thanks

jbunniii · Feb 21, 2012

(x - a) is a factor of both the numerator and the denominator. Try canceling it and see what results.

Dick · Feb 21, 2012

Or l'Hopital's theorem proves it easily. It's easy enough to prove that I don't think it rates it's own name or a place in reference books.

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