For each of the following functions, determine the order m of the zero of the deriva-tive f' at zo and show explicitly that the function is not one-to-one in any neighbor-hood of zo.(a) f(z) = z² + 2z + 1, zo = −1(b) f(z) = cos z, Zo = 0, ±, ±2л, ...(c) ƒ(z) = e²³, zo = 0

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Answered: For each of the following functions,…

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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For each of the following functions, determine the order m of the zero of the deriva- tive f' at zo and show explicitly that the function is not one-to-one in any neighbor- hood of zo. (a) f(z) = z² + 2z + 1, zo = −1 (b) f(z) = cos z, zo = 0, ±, ±2л,... (c) f(z) = e²³, zo = = 0