2. The Lorentzian function is a commonly encountered function in the study of resonance phenomena. It is defined according to f(r) with y>0. T 12 + (a) Sketch f(r) and f(r+ 10) graphically for circumstances in which Io > 0. (b) Determine the Maclaurin series of f(r) out to 2nd order in 1. Show your work. (c) Explain why a Maclaurin series (even one with lots and lots of terms!) cannot be used to verify the fact that the integral of f(1) between -0 and oo is equal to 1.
2. The Lorentzian function is a commonly encountered function in the study of resonance phenomena. It is defined according to f(r) with y>0. T 12 + (a) Sketch f(r) and f(r+ 10) graphically for circumstances in which Io > 0. (b) Determine the Maclaurin series of f(r) out to 2nd order in 1. Show your work. (c) Explain why a Maclaurin series (even one with lots and lots of terms!) cannot be used to verify the fact that the integral of f(1) between -0 and oo is equal to 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. The Lorentzian function is a commonly encountered function in the study of resonance
phenomena. It is defined according to
f(r)
with y>0.
T 12 +
(a) Sketch f(r) and f(r+ 10) graphically for circumstances in which Io > 0.
(b) Determine the Maclaurin series of f(r) out to 2nd order in 1. Show your work.
(c) Explain why a Maclaurin series (even one with lots and lots of terms!) cannot be used to
verify the fact that the integral of f(1) between -0 and oo is equal to 1.
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