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5. Suppose f(z) is entire and lim∞ (2) = 0. Show that f(2) is a constant function. Z 1(C) Hint: Use generalized Cauchy integral formula to show that f'(2) = 0. Note that (6-2)2 ƒ(C)/(C-z) and f(c) 5-2 = = - 1(0)15 1(C)/C (5-2)15 12/5 → ? as (∞. f(z) = c where c is some constant complex number. Show Z 6. Suppose f(z) is entire and limo that f(z) = cz+b. Hint: Apply question 5 with g(z) = f(z) — cz.

5. Suppose f(z) is entire and lim∞ (2) = 0. Show that f(2) is a constant function. Z 1(C) Hint: Use generalized Cauchy integral formula to show that f'(2) = 0. Note that (6-2)2 ƒ(C)/(C-z) and f(c) 5-2 = = - 1(0)15 1(C)/C (5-2)15 12/5 → ? as (∞. f(z) = c where c is some constant complex number. Show Z 6. Suppose f(z) is entire and limo that f(z) = cz+b. Hint: Apply question 5 with g(z) = f(z) — cz.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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5. Suppose f(z) is entire and lim∞ (2) = 0. Show that f(2) is a constant function. Z 1(C) Hint: Use generalized Cauchy integral formula to show that f'(2) = 0. Note that (6-2)2 ƒ(C)/(C-z) and f(c) 5-2 = = - 1(0)15 1(C)/C (5-2)15 12/5 → ? as (∞. f(z) = c where c is some constant complex number. Show Z 6. Suppose f(z) is entire and limo that f(z) = cz+b. Hint: Apply question 5 with g(z) = f(z) — cz.
Transcribed Image Text:5. Suppose f(z) is entire and lim∞ (2) = 0. Show that f(2) is a constant function. Z 1(C) Hint: Use generalized Cauchy integral formula to show that f'(2) = 0. Note that (6-2)2 ƒ(C)/(C-z) and f(c) 5-2 = = - 1(0)15 1(C)/C (5-2)15 12/5 → ? as (∞. f(z) = c where c is some constant complex number. Show Z 6. Suppose f(z) is entire and limo that f(z) = cz+b. Hint: Apply question 5 with g(z) = f(z) — cz.
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