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Let be a function for which all directional derivatives at all points exist. Define a new function by the formula. Given these conditions, which of the statements below is correct?

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MCQs on Real Analysis.


Let<br><img src='https://www.fatskills.com/images2/GradExams/283E8FD1-0054-446A-9214-AF88BD1A2688.png' height='21' width='95'/> be a function for which all directional derivatives at all points exist. Define a new function<br><img src='https://www.fatskills.com/images2/GradExams/9610CA3F-7430-4D3A-BFBF-8F3EF82028F2.png' height='18' width='86'/> by the formula<br><img src='https://www.fatskills.com/images2/GradExams/5D776376-11FC-4399-839E-6378C3D2998C.png' height='20' width='229'/>. Given these conditions, which of the statements below is correct?





 
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