Science:Math Exam Resources/Courses/MATH100/December 2018/Question 03
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Question 03 

Compute the following limit or prove that it 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 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 

Take to the function and find its limit. 
Hint 2 

You might need to use L'Hôpital's Rule, possibly more than once. 
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. We denote the limit by and next we compute
We see that represented as a quotient above, then the limit for is of the form and so, we apply L'Hôpital's Rule:
This limit is of the form , so we apply again L'Hôpital's Rule and obtain:
Since , we conclude that . 