Science:Math Exam Resources/Courses/MATH100/December 2015/Question 07
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Question 07 

Is the function differentiable at ? You must explain your answer using the definition of the derivative. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Recall the definition of differentiability at some point. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. First, we check that is continuous at 0. (Note that if is not continuous at 0, is not differentiable at 0.) Using , we can compute the right hand limit as On other hand, it is easy to get Therefore, is continuous at 0. Now, we show is differentiable at 0. By its definition, first consider the left hand limit: The last inequality follows from Then, the right hand limit can be computed as

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Nobody voted on this yet Hard Easy 