Calculus please answer d and e Consider the complex function f(2)= ( ² + ²) ². a) Show its Laurent series about :=0 is g

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Calculus Please Answer D And E Consider The Complex Function F 2 A Show Its Laurent Series About 0 Is G 1 (21.81 KiB) Viewed 14 times

Calculus please answer d and e Consider the complex function f(2)= ( ² + ²) ². a) Show its Laurent series about :=0 is given by f(=) - Σ 24 (2n)! m!(2n-m)!7 [6] Hom b) Compute its residue at the origin. [2] c) Taking the contour 7 to be the positively oriented unit circle, state why Cauchy's Integral Formula cannot be applied as is to evaluate the integral f(=) [2] d) Use the Laurent Series of section a) to evaluate the integral instead. [8] e) Finally, deduce now that [cost cost ode= = (2n)! 23 (!) TEN 2-2 E [7] F