Science:Math Exam Resources/Courses/MATH110/April 2014/Question 02 (b)
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Question 02 (b) 

Find . 
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 

We can check whether L’Hopital’s rule applies here. 
Hint 2 

We can divide through by the highest power of and then simplify. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Direct substitution gives “” so we can use L’Hopital’s rule again (and again):

Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We can also divide by the highest power to get:
To get the same result by noting that grows faster than . 