2 2.Suppose g: [0, 1] → C is a continuous function g(t) in one real variable. Define a complex functionf: U → C where U = C\ [0, 1], by(a) For a, z EU, show thatf(x) =g(t)t-zdt.g(t)f(z)-f(a)=- L₁ (²₁(t-z)(t-a)(b) Show that f is holomorphic on U and find an expression for the derivative f'(a).(z-a).dt.

Given: g:0,1→ℂ is a continuous real valued function. Define a complex function: f: U→ℂ where U=ℂ \…

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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