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The rule is a method for finding the limiting behavior of a rational function whose numerator and denominator tend to zero at a point or if both functions diverge to infinity also.
For example, the limit of the function as the value of x --> 2.
This meets the conditions since both the numerator and denominator approach 0 as the value of x -->2. The rule states that in such cases, one can take the derivative of the numerator and denominator independently and then find the limit of this ratio. Since the derivative of the numerator is 2x, and the derivative of the denominator is 1, the ratio of the derivatives is the experession 2x/1 or just 2x; and the limit as x approaches two for this function is just 2(2) = 4. In the area near x=2, the value of the original ratio is very near 4.
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