## Abstract

We return to the question of the existence of a primitive function of *f* (*x*) = 1/*x* for *x* > 0 posed above. Since the function *f*(*x*) = 1/*x* is Lipschitz continuous on any given interval [*a*, *b*] with 0 < *a* < *b*, we know by the Fundamental Theorem that there is a unique function *u*(*x*) which satisfies u′(*x*) = 1/*x* for a ≤ x ≤ b and takes on a specific value at some point in [*a*, *b*], for example *u*(1) = 0. Since *a* > 0 may be chosen as small as we please and *b* as large as we please, we may consider the function *u*(*x*) to be defined for *x* > 0.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2004