Science:Math Exam Resources/Courses/MATH110/December 2013/Question 01 (b)
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Question 01 (b) 

Determine whether the following statement is true or false. If it is true, provide justification. If it is false, provide a counterexample. b) If , then . 
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 

The key observation in this problem is to note that the function is not necessarily continuous! Try to find a counter example where the function is not continuous. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. False: The easiest way to see this is to come up with a function where the limit exists but the function is not defined there. For example . The limit exists and is equal to but is not in the domain, so is not defined. Hence the statement is false. 