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Question: in the last part 4 a4...

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In the last part 4. a=4.
(20 points) For the Maclaurin series: (2n+1)! 51 7 (1) Using differentiation formula cosz - (sin zy, differentiate each side () to find the Maclaurin series for the function cosz. of equation (2) By replacing by in equation ) to find the Laurent series of function e)sinin the domain 0<to (3) Using the Laurent series of f(z)of sin㈢ in (2) to find the residue at z=0 : Res [f(z), 0] sin㈢dz ,Cis the (4) Using the result of (3) (residue) to evaluate the integral positively oriented circle |za.
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