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Suppose the real Fourier series for on is given by .Which of the following statements is false? I. If, then this series converges pointwise on. II. III. If, for any, then is an even function.

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MCQs on Partial Differential Equations.


Suppose the real Fourier series for<br><img src='https://www.fatskills.com/images2/GradExams/203085BB-4CDE-402E-A5EC-575C34B85EBF.png' height='18' width='10'/> on<br><img src='https://www.fatskills.com/images2/GradExams/E44B712C-6F4D-4655-9D3D-2D71F0A571A3.png' height='20' width='54'/> is given by <br><img src='https://www.fatskills.com/images2/GradExams/DCFA8AC0-6CA5-43E9-BEA9-36A127ADD1AE.png' height='21' width='278'/>.<br/>Which of the following statements is false?<br/> I. If<br><img src='https://www.fatskills.com/images2/GradExams/D1B9A2A8-EA04-4C21-A9B3-19E7F069DB7D.png' height='22' width='119'/>, then this series converges pointwise on<br><img src='https://www.fatskills.com/images2/GradExams/64EEAE0F-4B21-4677-9771-6E808BA780FD.png' height='20' width='59'/>.<br/> II.<br><img src='https://www.fatskills.com/images2/GradExams/0DCB773E-24FC-4F78-9060-EDC04C26ADA0.png' height='24' width='210'/><br/> III. If<br><img src='https://www.fatskills.com/images2/GradExams/62847E4C-1461-4EFD-93D0-9623FEBB2530.png' height='40' width='182'/>, for any<br><img src='https://www.fatskills.com/images2/GradExams/D8F0A0B9-3DDB-449C-98D9-B0C3C134E282.png' height='10' width='11'/>, then<br><img src='https://www.fatskills.com/images2/GradExams/203085BB-4CDE-402E-A5EC-575C34B85EBF.png' height='18' width='10'/> is an even function.





 
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