Science:Math Exam Resources/Courses/MATH105/April 2011/Question 09 (c)
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Question 09 (c) 

Each of the shortanswer questions below is worth 5 points. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work. Express the limit as a definite integral, and leave it in the form of an integral. Do not evaluate it! 
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 

The Riemann sum formula using the right end points for a function is
where

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 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. The Riemann sum formula using the right end points for a function is
where
In our example, comparing the terms, we see that
and so
Also, we have that
So taking , we have
so we have and hence since and so . Plugging all this information in, we have 
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. The Riemann sum formula using the right end points for a function is
where
In our example, comparing the terms, we see that
and so
Also, we have that
So taking , we have
so we have and hence since and so giving . Plugging all this information in, we have 