Consider the multivalued function for ���-1� given in Eq. sin-'z=-ilog(zi+(l-z ) ). Show that if � is a real number satisfying -1≤�≤1, then all possible branches of this function yield a real value for the inverse sine of �.

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
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Consider the multivalued function for ���-1� given in Eq. sin-'z=-ilog(zi+(l-z ) ). Show that if � is a real
number satisfying -1≤�≤1, then all possible branches of this function yield a real
value for the inverse sine of �.
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