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I would appreciate any help on how to do this, thanks!

Please see file attached...

(z,r) is a circular contour of radius r>0 centred at z

Explain why

cannot be evaluated by applying Cauchy's integral formula with
, when = 1. Hence evaluate the integral.


Solution Preview

Observe that the function f(x, y) = (x, 0) is differentiable as a real-valued function,
but not differentiable when viewed as a complex function, i.e. f(z) = Re(z)
is not analytic (as neither is the ...

Solution Summary

This explains why a given integral cannot be evaluated using Cauchy's formula and how to evaluate the integral.