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To: Joe NYC who wrote (151100)	12/5/2001 3:35:45 PM
From: brushwud	Read Replies (2) \| Respond to of 186894

Re: When you have a ratio of functions that evaluates to 0/0, what you could do is differentiate both the numerator and the denominator, then calculate the results using the newly derived formulas. That's a good answer. I tested it on (x - 1) / (X^2 - 1) which is 0 as x approaches 1. Differentiating I get 1 / 2, which is 0.5 I put together a simple Excel spreadsheet, by starting form 0.9, and incrementing by previous result + (1 - previous result) / 2, the ratio of the functions do converge to 0.5 What he described is L'Hopital's Rule from calculus. But you could have done it the algebra way: (x - 1)/(x^2 - 1) = (x-1)/[(x + 1)(x - 1)] = 1/(x + 1) This reminds me of a puzzle which is solved by the mathematician using calculus, by the physicist using algebra, and by the engineer using computer simulation. (The physicist's way is best, but as John von Neumann expressed, "It isn't any faster.")