MATH101 April 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 • Q9 •
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!
|
[show]Hint
|
The previous part of this question gives us the value of the Simpson's rule approximation. Find the worst value the error can be and then sum this worst value with the approximation from the previous part.
|
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.
- If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
- If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
|
[show]Solution
|
Using the hint, we plug in into the error bound and notice that the error lies between
Evaluating these bounds, we get that
and one last simplification yields
.
Now, let's use the the approximation and notice that by definition, we have that
Notice that in magnitude, the value
and so we have that the largest the integral can be is the approximation added onto this largest error bound. This gives
completing the question.
|
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Simpson's rule, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag
|
Math Learning Centre
- A space to study math together.
- Free math graduate and undergraduate TA support.
- Mon - Fri: 12 pm - 5 pm in MATH 102 and 5 pm - 7 pm online through Canvas.
|