Science:Math Exam Resources/Courses/MATH104/December 2011/Question 01 (a)
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Question 01 (a) 

Compute 
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 

How can we use conjugates to deal with the square root in the bottom? 
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 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. The limit evaluates to the form 0/0, which is undefined. However, notice that in the denominator we can get rid of the square root by multiplying top and bottom by the conjugate Now notice that the quadratic polynomial on the top can factor, and therefore Therefore 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. The limit evaluates to the form 0/0, which is undefined. 0/0 is a form for which we can apply l'Hospital's rule (if you know it): 
Solution 3 

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Please rate my easiness! It's quick and helps everyone guide their studies. We can be a bit clever and factor then factor as a difference of squares where we think of as the square of . Hence
Combining gives 