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Single Degree-of-Freedom Undamped Vibration
Published in Haym Benaroya, Mark Nagurka, Seon Han, Mechanical Vibration, 2017
Haym Benaroya, Mark Nagurka, Seon Han
He is best known for developing the rule which bears his name for finding the limit of a rational function whose numerator and denominator tend to zero at a point. L’Hôpital’s rule uses derivatives to help evaluate limits involving indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit. L’Hôpital’s rule first appeared in his book.
Field calibration and validation of a pavement aging model
Published in International Journal of Pavement Engineering, 2022
Nooralhuda F. Saleh, Elizabeth Braswell, Michael Elwardany, Farhad Yousefi Rad, Cassie Castorena, Y. Richard Kim
The rational function provides the desired gradient shape with depth (condition 2). At the pavement surface (depth of zero), n1 becomes equal to the constant regression parameter b2. Thus, b2 represents the maximum log |G*| value that can be achieved at the pavement surface (condition 6). For infinite depth, n1 becomes equal to b1 (using L’Hopital's Rule to evaluate the limit at the indeterminate form). Accordingly, b1 acts as the asymptote with depth (condition 3) for the function n1. With increasing time (i.e. with increasing APt), APfield at infinite depth increases until it reaches a maximum at infinite time. Therefore, the overall asymptote with depth for APfield increases with time, satisfying condition 4.
Examining the pedagogical content knowledge of prospective mathematics teachers on the subject of limits
Published in International Journal of Mathematical Education in Science and Technology, 2021
Feyza Aliustaoğlu, Abdulkadir Tuna
When examining the answer given by the MTC, it was observed that the MTC did not indicate the accurate answer, and also that the MTC did not completely express the cause of this mistake. The student assumed that ‘limit’ denotes replacement of the value in the function and marked the answer as zero upon observing both the numerator and denominator in the question to be zero. However, here is indeterminate, and it has to be eliminated to find a result. To do so, the denominator has to be factorized; to find the limit, the indeterminate form can be eliminated by multiplying the numerator and denominator with the conjugate of the denominator.