2. Let f be the branch of z¹/4 such that 2 > 0 and 0 < arg z < 27. Let C denote the semi-circular path 2=2e¹0 (0 ≤0 ≤ π). (a) Show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]2'(0) exist and calculate their values. [ f(z) dz. (b) Calculate
2. Let f be the branch of z¹/4 such that 2 > 0 and 0 < arg z < 27. Let C denote the semi-circular path 2=2e¹0 (0 ≤0 ≤ π). (a) Show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]2'(0) exist and calculate their values. [ f(z) dz. (b) Calculate
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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Please help with Question 2 (a), (b) and (c)
![2. Let f be the branch of z¹/4 such that |z| > 0 and 0 < arg z < 2π. Let C denote the semi-circular path
2=2e¹0 (0 ≤ 0 ≤ π).
(a) Show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]z'(0) exist and
calculate their values.
(b) Calculate Jo
f(z) dz.
(c) Why did we show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]z′(0)
exist before calculating [ƒ(z) dz?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94ea00a2-f5ad-495c-94c7-735caa6aac17%2F300ee128-ca94-49dd-8cb9-97a5fb59b04c%2Fd8f9vej_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let f be the branch of z¹/4 such that |z| > 0 and 0 < arg z < 2π. Let C denote the semi-circular path
2=2e¹0 (0 ≤ 0 ≤ π).
(a) Show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]z'(0) exist and
calculate their values.
(b) Calculate Jo
f(z) dz.
(c) Why did we show that the right hand limits at 0 = 0 of the real and imaginary parts of f[z(0)]z′(0)
exist before calculating [ƒ(z) dz?
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