(a) Consider the integral I (k) = S − k (t² + 2/3) e dt, k > 0. 1+t Find the first term in the asymptotic expansion of I(k) as k → ∞.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.5: Properties Of Logarithms
Problem 68E
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(a) Consider the integral
I (k) = S
− k (t² + 2/3)
e
dt,
k > 0.
1+t
Find the first term in the asymptotic expansion of I(k) as k → ∞.
Transcribed Image Text:(a) Consider the integral I (k) = S − k (t² + 2/3) e dt, k > 0. 1+t Find the first term in the asymptotic expansion of I(k) as k → ∞.
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