KNOWLEDGEBASE - ARTICLE #2139

The function X/(1 - exp(-K*X)) when X is zero

The function X/(1 - exp(-K*X)) appears in some kinetic equations. It is a standard equation, easy for Prism or any program to evaluate. Except when X is zero. The denominator becomes 0.0 so it is impossible to calculate. But is it? The numerator is also 0.0. 

The rule of de l'Hopital tells us that the limit of [X/(1-exp(-K*X))] as X approaches zero is 1/K

So the function can be evaluated -- even when X=0 -- by rewriting it like as shown below. Of course, you'll need to define K in earlier lines of the equation and use B in later lines as part of a larger model. 

A = 1-exp(-K*X)
B = IF(A=0, 1/K, X/A)

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