Science:Math Exam Resources/Courses/MATH110/December 2014/Question 02 (b)
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Question 02 (b) 

Determine whether each of the following statements is true or false. If it is true, provide justification. If it is false, provide a counterexample. Answers without justification will receive no marks. (b) The limit does not exist. 
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 that exists if and only if . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that exists if and only if . First, we evaluate the left hand limit; Since , we consider . In this range, , so that we get
Now, we compute the right hand limit; Since , we consider . In this range, , so that we get
Collecting the terms, we have . As a result, the limit doesn't exist. . 