MATH105 April 2015
• 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 (d)
is a left Riemann sum for a function on the interval with sub intervals. Find the values of , and .
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!
Recall that a left Riemann sum for on with subintervals takes the form
Compare the given sum to this formula.
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We compare the given sum to the formula for a left Riemann sum (see hint 1):
From comparing the two formulas, we see that that and
Furthermore, since the first term of the left Riemann sum is , then .
Finally, rearranging the equation for we obtain .