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 (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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