1- Determined the singularity of the following functions and classification cos z a) f(z) = z2 sin z b) f(z) : 1-cos z5 2- Show that the function f (z) = has a removable singularity at zo sin z3 and that when the singularity is removed the resulting function has a zero of order 7. 3- Let y be the arc of the circle z 1 from z = 2 to z = 2i Show that dz z2 where y = {z : \z| = 4- Evaluate (z+2)(z-1} 4| = } log z dz , where y = {z : ]z – i| i- z 5- Evaluate

1- Determined the singularity of the following functions and classification cos z a) f(z) = z2 sin z b) f(z) : 1-cos z5 2- Show that the function f (z) = has a removable singularity at zo sin z3 and that when the singularity is removed the resulting function has a zero of order 7. 3- Let y be the arc of the circle z 1 from z = 2 to z = 2i Show that dz z2 where y = {z : \z| = 4- Evaluate (z+2)(z-1} 4| = } log z dz , where y = {z : ]z – i| i- z 5- Evaluate

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 34E

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