Consider the integral f(x) = · Lezh exh(t) q(t) dt where the function h is real-valued and where h and q are assumed to be differentiable as many times as needed in the analysis. Assume, further, that h(t) attains an absolute maximum at the interior point to for which we have h" (to) < 0. Show that the first term in the asymptotic expansion off as x ∞ is q(to)exh (to) -2π 1/2 xh" (to). and write out the next term.

Consider the integral f(x) = · Lezh exh(t) q(t) dt where the function h is real-valued and where h and q are assumed to be differentiable as many times as needed in the analysis. Assume, further, that h(t) attains an absolute maximum at the interior point to for which we have h" (to) < 0. Show that the first term in the asymptotic expansion off as x ∞ is q(to)exh (to) -2π 1/2 xh" (to). and write out the next term.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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