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The Convergence Behavior of a One-Parameter Family
Let
, for
. For any
,
. Moreover:
1. If
, then
is strictly increasing.
2. If
, then
is strictly decreasing.
3. If
, then
has exactly one local minimum and it is the absolute minimum.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
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Reference: C. X. Kang and E. Yi, "The convergence behavior of
,"
The College Mathematics Journal
,
38
(5), 2007 pp. 385–386.
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"
The Convergence Behavior of a One-Parameter Family
" from
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http://demonstrations.wolfram.com/TheConvergenceBehaviorOfAOneParameterFamily/
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
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