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paddo
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How would you integrate sin(z)/(z-1)^2 using Cauchy's Integral Formula? 1 is in C.
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Cauchy's Integral Formula is a fundamental theorem in complex analysis that relates the values of a holomorphic function inside a closed curve to its values on the curve itself.
The main problem associated with Cauchy's Integral Formula is finding the integral of a function along a given curve, which can be a challenging task in some cases.
Cauchy's Integral Formula is significant because it provides a powerful tool for evaluating complex integrals and has many applications in mathematics, physics, and engineering.
Cauchy's Integral Formula calculates the integral of a function along a closed curve, while Cauchy's Residue Theorem is used to calculate integrals of functions with singularities inside a closed curve.
Cauchy's Integral Formula is closely related to the Cauchy-Riemann equations, which describe the conditions for a function to be holomorphic. The existence of a complex derivative is a consequence of these equations and is necessary for Cauchy's Integral Formula to hold.