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The Convergence Behavior of a One-Parameter Family

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Let , for . For any , . Moreover:

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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.

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Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA

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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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