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Let be differentiable and let and (in particular these limits exist). Which of the following implies the existence of for which?

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Let<br><img src='https://www.fatskills.com/images2/GradExams/8449C6E3-B0BF-41A9-BF4A-7D0F59D6F65F.png' height='20' width='126'/> be differentiable and let<br><img src='https://www.fatskills.com/images2/GradExams/B42A826D-28AC-4F13-BE54-5DE2EB077E33.png' height='20' width='154'/> and<br><img src='https://www.fatskills.com/images2/GradExams/411D842F-9395-412D-9FBE-494E8EAB87EE.png' height='20' width='150'/> (in particular these limits exist). Which of the following implies the existence of<br><img src='https://www.fatskills.com/images2/GradExams/1E66C631-4B49-403C-821F-FC5ED6EFD1F4.png' height='20' width='85'/> for which<br><img src='https://www.fatskills.com/images2/GradExams/F226F5DF-1C73-4061-8818-1B7FEF375681.png' height='21' width='74'/>?






 
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