The path C1 from the origin to the point z =1 along the graphof the function def

Question

The path C1 from the origin to the point z =1 along the graphof the function defined by means of the equations y(x) = { x^3 sin(/x) when 0 < x <= 1,                            0                   whenx = 0 is a smooth arc that intersects the real axis an infinitenumber of times. Let C2 denote the line segment along the real axis from z=1 back to the origin, and let C3denote any smootharc from the origin to z=1 that does not intersect itself and has only its end points incommon with the arcs C1 and C2. Apply Cauchy-Goursat theorem to show that if a function f is entire,then Conclude that, even though the closed contour C = C1 + C2intersects itself an infinite number of times, The Cauchy-Goursat theorem. If a function f is analytic at all points interior to and on asimple closed contour C, then The Cauchy-Goursat theorem can be extended in the followingway, involving a simply connected domain. If a function f is analytic throughout a simply connecteddomain D, then

Explanation / Answer

can you tell me precisely what the cauchy goursat thm. says? my book doesnt call it that, but i m sure it has it.

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