Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 01 (b)
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Question 01 (b) 

(b) Calculate . 
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 L'Hôpital's rule: for indeterminate limits of the form or , differentiate both the numerator and denominator. 
Hint 2 

Use chain rule when differentiating the denominator. 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. If we use direct substitution, we get form, so that we need to use L’Hôpital’s rule. Recall the facts and, using the chain rule with , , and , that Therefore, since ,
Here, the first equality follows from L’Hôpital’s rule.
Answer: . 