This function is defined on
.
The function
is the composition of
on a rational function; hence it is differentiable on its domain. We have:
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The denominator never vanishes and is positive at every point of the domain, thus
increases over
and over
.
The function
is a rational function; hence it is differentiable on its domain. We have:
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Let us now compute the limits of
at the open endpoints of its domain.
Noah Dana-Picard 2007-12-28