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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 27CR
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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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