Science:Math Exam Resources/Courses/MATH100/December 2016/Question 05 (c)
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Question 05 (c) 

Compute the limit . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Use the trigonometric identity 
Hint 2 

You can also use l'Hopital's rule. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Using trigonometric identity , the given function can be written as
Since we have , by the continuity of the square function, we obtain the desired limit as

Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. Apply L’Hopital's rule twice. Then, we get
