Let be a function on an open set with singularities at . Let be a closed curve in . Which of the conditions below is not necessary for the following formula to hold?

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Let <br><img src='https://www.fatskills.com/images2/GradExams/EE65EA53-50A0-4D19-A4F5-2B1E6D50FA0E.png' height='18' width='10'/> be a function on an open set <br><img src='https://www.fatskills.com/images2/GradExams/9C120967-EA32-4F9E-82B5-140DB0D4A8BA.png' height='15' width='56'/> with singularities at <br><img src='https://www.fatskills.com/images2/GradExams/ECBF91D7-1CE2-4D6B-9AE9-8A8B09DE9CF5.png' height='20' width='101'/>. Let <br><img src='https://www.fatskills.com/images2/GradExams/452C0AB5-8299-4CBB-A7CA-A18BF98C1978.png' height='14' width='11'/> be a closed curve in <br><img src='https://www.fatskills.com/images2/GradExams/3139DCFF-5F67-4EB8-BD0F-66C1B91BE24A.png' height='15' width='14'/>. Which of the conditions below is not necessary for the following formula to hold? <br><img src='https://www.fatskills.com/images2/GradExams/F406DA9D-44B3-43BB-B80C-FB6BA1990089.png' height='29' width='270'/>