ERIC Number: EJ892208
Record Type: Journal
Publication Date: 2010
Abstractor: As Provided
Reference Count: 3
Generalizing a Limit Description of the Natural Logarithm
Dobbs, David E.
International Journal of Mathematical Education in Science and Technology, v41 n5 p687-691 2010
If f is a continuous positive-valued function defined on the closed interval from a to x and if k[subscript 0] is greater than 0, then lim[subscript k[right arrow]0[superscript +] [integral][superscript x] [subscript a] f (t)[superscript k-k[subscript 0]] dt= [integral][superscript x] [subscript a] f (t)[superscript -k[subscript 0] dt. This generalizes a result of Finlayson describing ln(x) as a certain limit. Applications include new descriptions of arcsin(x) and arctan(x) as limits. This note could find use as an enrichment material in an introductory calculus course in the unit(s) introducing the Riemann integral and its applications.
Descriptors: Calculus, Numbers, Intervals, Introductory Courses, College Mathematics, Computation, Mathematical Logic, Validity, Mathematics Education
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Authoring Institution: N/A