Science:Math Exam Resources/Courses/MATH110/April 2011/Question 02 (a)
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Question 02 (a) 

Evaluate the following limit, if it exists. 
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 

Try evaluating the limit as written. Which rule can you apply to the limit based on the answer you get? 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. Simply trying to evaluate the limit as written gives the following: This is an indeterminate form and means that we can use L'Hopital's Rule. Differentiating the numerator and denominator of the function, we get the new limit: Simply evaluating this limit gives which is also the value of the original limit. 