This function is defined on
.
The function
is the composition of a rational function on the exponential; thus, it is differentiable on its domain. We have:
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Let us compute the limits of
at the open ends of the domain:
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As the exponential function with basis
has
as its limit at
, we need some lagberaic work. We have:
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At
, we need to compute one-sided limits:
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|
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Let us now compute the second derivative of
:
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We display the graph of
in Figure 4.
Noah Dana-Picard 2007-12-28