MATH101 April 2012
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Question 07 (c)
Let . Without computing I, find an upper bound for . You may use the fact that if on the interval , then the error in using Sn to approximate has absolute value less than or equal to .
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!
As it says in the question statement, given , an even integer, and an upper bound for all in the interval , the error that comes from using Simpson's Rule is as follows:
How would you find K?
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We will use the hint in the statement of the problem: if we can find an upper bound K on , then we know that .
First we find an upper bound on .
On our interval of integration, [1,2], . So our upper bound on is K = 24.
Now we simply plug this into the error formula given above to get:
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Simpson's rule