2. Suppose g: [0, 1] → C is a continuous function g(t) in one real variable. Define a complex function J: U → C where U = C\ [0, 1], by (a) For a, z EU, show that S(z) = f' g(t) Z dt. g(t) √(z) - ƒ(a) = f'(z-a). (t-z)(t-a) (b) Show that f is holomorphic on U and find an expression for the derivative f'(a). dt.
2. Suppose g: [0, 1] → C is a continuous function g(t) in one real variable. Define a complex function J: U → C where U = C\ [0, 1], by (a) For a, z EU, show that S(z) = f' g(t) Z dt. g(t) √(z) - ƒ(a) = f'(z-a). (t-z)(t-a) (b) Show that f is holomorphic on U and find an expression for the derivative f'(a). dt.
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 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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