MATH105 April 2012
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Question 08 (f)
Short-answer questions. No credit will be given for the answer (even if it is correct) without the accompanying work.
Find a bound for the error in approximating
using Simpson’s rule with n = 6 subintervals. There is no need to simplify your answer.
Do not write down the Simpson’s rule approximation Sn.
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 if on the interval , then the error in using to approximate has absolute value less than or equal to .
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The error bound for Simpson's rule requires us to find the fourth derivative of the integrand.
For , we find:
To find our K, we need to know the largest can be over the integration range .
is a decreasing function, with its largest value on being at , so K = 16.
The error with is bounded by .
Note: the question did not ask us to evaluate the Simpson's rule approximation; we were only asked to bound its error.
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