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5. Let C, denote the semicircle of radius r, centered at the origin and going clockwise from z = r to z = -r in the upper half plane. Find (with explanation) real numbers M1 and M2 so that Log(2)dz < M1, Log(2)dz + 448 z2 + 448 < M2 103 22 C10-3 Hints: you could think of the contours as CR and Ce respectively, with R= 103 and € = 10-3. This problem is about estimates only. Don't worry about residues,

5. Let C, denote the semicircle of radius r, centered at the origin and going clockwise from z = r to z = -r in the upper half plane. Find (with explanation) real numbers M1 and M2 so that Log(2)dz < M1, Log(2)dz + 448 z2 + 448 < M2 103 22 C10-3 Hints: you could think of the contours as CR and Ce respectively, with R= 103 and € = 10-3. This problem is about estimates only. Don't worry about residues,

Advanced Engineering Mathematics
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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5. Let C, denote the semicircle of radius r, centered at the origin and going clockwise from z = r to z = -r in the upper half plane. Find (with explanation) real numbers M1 and M, so that Log(2)dz Log(z)dz < M1, < M2 z2 + 448 z2 + 448 C10-3 103 Hints: you could think of the contours as CR and Ce respectively, with R = 103 and € = 10-3. This problem is about estimates only. Don't worry about residues, antiderivatives, or about simplifying your answers numerically.
Transcribed Image Text:5. Let C, denote the semicircle of radius r, centered at the origin and going clockwise from z = r to z = -r in the upper half plane. Find (with explanation) real numbers M1 and M, so that Log(2)dz Log(z)dz < M1, < M2 z2 + 448 z2 + 448 C10-3 103 Hints: you could think of the contours as CR and Ce respectively, with R = 103 and € = 10-3. This problem is about estimates only. Don't worry about residues, antiderivatives, or about simplifying your answers numerically.
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