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In Problems 5-10, determine the zeros and their order for the given function. 5. f (2) = (2+2-2)2 6. f(z) = 24-16 7. f (z) = 24+22 8. f(z) = sin z 9. f(2) = e23 - ez 10. f(2) = ze - z In Problems 11-14, the indicated number is a zero of the given function. Use a Maclaurin or Taylor series to determine the order of the zero. 11. f(2) = z(1 - cos' z); z =0 12. f(z) = z - sin z; z = 0 13. f(2) = 1 -e#-1; z =1 14. f(2) = 1 - mi + z + e; z =mi In Problems 15-26, determine the order of the poles for the given function. 15. f(2) = 3z - 1 22 + 2z +5 16. f(2) = 5- 6 22 1 + 4i z-1 17. f (z) = 7 ( z + 2 ) ( 2 + 1 ) 4 18. f(z) = (z + 1) (23 + 1) 19. f(z) = tan z 20. f(2) = cot TZ 22 21. f(2) = 1 - cosh z 22. f ( 2) = 24 23. f(z) = 1tez 24. f(2) = 22 sin z 25. f(z) = 2 2 26. f(z) = COS Z - cos 2z 26 In Problems 27 and 28, show that the indicated number is an essential singularity of the given function. 27. f(2) = 23 sin ; 2 =0 28. f(z) = (z -1) cos 27212 = - 2 29. Determine whether z = 0 is an essential singularity of f(2) = ez+1/z. 30. Determine whether z = 0 is an isolated or non-isolated singularity of f (z) = tan (1/z)