Science:Math Exam Resources/Courses/MATH100/December 2011/Question 01 (b)
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Question 01 (b) 

ShortAnswer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answers. Unless otherwise stated, it is not necessary to simplify your answers in this question. Evaluate or determine that 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 

If you try to evaluate the limit directly, you end up with 0/0, which means we cannot conclude anything for the moment. Factorizing would be a great idea but because of the square root it is not possible. Hence, how could we 'get rid' of the square root at the numerator? 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. If you try to evaluate the limit directly, you end up with 0/0, which means we cannot conclude anything for the moment, more work needs to be done. Since we have a square root, we will multiply on each side of the fraction by the conjugate in the hope to simplify things: 