Science:Math Exam Resources/Courses/MATH105/April 2013/Question 01 (d)
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Question 01 (d) 

ShortAnswer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Fill in the blanks with right, left, or midpoint; an interval; and a value of . is a _________ Riemann sum for on the interval [____ , ____] with ______. 
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 left Riemann sum of a function ƒ over the interval [a,b] with n intervals is given by with
The midpoint Riemann sum of a function ƒ over the interval [a,b] with n intervals is given by with
The right Riemann sum of a function ƒ over the interval [a,b] with n intervals is given by or with 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. There are multiple correct answers to this problem. The following is but one of three possible interpretations: This is a left Riemann sum from 1.5 to 5.5 with rectangles. If we look at our left endpoint formula in the hint, we realize that This last relation tells us that b=n+a=5.5. 
Solution 2 

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Please rate my easiness! It's quick and helps everyone guide their studies. There are multiple correct answers to this problem. The following is but one of three possible interpretations: This is a midpoint Riemann sum from 1 to 5 with rectangles. We can recognize this by writing which is in the form of our midpoint formula in the hint if we take This last relation tells us that b=n+a=5. 
Solution 3 

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Please rate my easiness! It's quick and helps everyone guide their studies. There are multiple correct answers to this problem. The following is but one of three possible interpretations: This is a right endpoint Riemann sum from 0.5 to 4.5 with rectangles. We can recognize this by writing which is in the form of our right endpoint formula in the hint if we take This last relation tells us that b=n+a=4.5. 