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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

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

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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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
Transcribed Image Text: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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