Science:Math Exam Resources/Courses/MATH105/April 2015/Question 01 (n)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q1 (l) • Q1 (m) • Q1 (n) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) •
Question 01 (n) 

Find the limit of the sequence . 
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 

To find the limit of the sequence , evaluate

Hint 2 

Recall that

Hint 3 

If you get stuck when evaluating a limit, try considering 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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. To find the limit of the sequence we'll need to evaluate By the product rule for logarithms, , so this limit is equivalent to . We can begin by computing (by continuity of the logarithm). First, note that by using the substitution , Now, we can apply L'Hôpital's rule for indeterminate forms (i.e., limits of the form ) to compute , since substituting into yields . L'Hôpital's Rule's rule gives Hence, Therefore,
