MTH 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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question form
MTH 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I've come across a couple of more problems that are troublesome and I wonder if they are legitimate questions for this test. There was a brief encounter with the Taylor series in the notes but not in the text for the section on the test. There is a question asking about the E(x) function and in the notes you say we'll get to it later and that makes me wonder why this question is showing up here. Also there is a question about Nested Interval theorem and I this isn't even in the book.There is also a question about the Intermediate Value Theorem and this wasn't in the sections we covered either.I've pasted the questions below.
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Prove that if E(x) is the error in the local linearization (i.e., the tangent-line approximation) of f(x) in the vicinity of x = a, then lim{x -> 0 } [ E(x) / (x-a) ] = 0. Explain why this result is significant and important.
This question is legitimate. The tangent-line approximation is covered in an upcoming qa assignment, and E(x) is just the difference between the tangent-line approximation and the actual value of the function being approximated. This will make more sense to you soon. You might consider bringing this question up again after completing the qa on the tangent-line approximation.
Explain why continuity is essential in the proof of the Intermediate Value Theorem, which states that if f(x) is continuous on [a, b] then it takes every value between f(a) and f(b).
The Intermediate Value Theorem comes up in the first chapter, as does the concept of continuity (both in section 1.7).
Check out those definitions, then explain what you do and do not understand about those definitions and how they apply to this question.
When proving that continuous functions are integrable, we must show that by making intervals small enough the difference between upper sums and lower sums on an interval can be made as small as desired. Explain how we do this using successive subdivisions of the interval [a, b] of integration. In particular explain how the Nested Interval Theorem and the definition of continuity are used.
This is covered in Asst 17, in section 5.4. The part about the nested interval theorem has been left out of the current edition of the text and you won't be expected at this point to answer that part.
Explain why continuity is essential in the proof of the Intermediate Value Theorem, which states that if f(x) is continuous on [a, b] then it takes every value between f(a) and f(b).
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Maybe these are things we should know generally but they do seem beyond the scope of the sections covered. Regardless I just want to be sure if these questions were supposed to be here so that I can investigate them further. I have delayed taking my test until Monday to give me more time to study and get what answers you can give me to these and the previous questions I submitted. I know this is a test and you can only say so much about the questions but whatever can you do to help clear this up is appreciated. Thank you.
Test 1 isn't scheduled until after you have completed Assignment 17, which should be completed by the 12th. The test could be completed during the following week.
I apologize for the delayed posting of this file. I completed my review on 7/3, but the posting process apparently went awry and it is being posted two days late. It might therefore be a little out of order on your access page.
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The above is the last question form I submitted asking about questions on this next test. Your answers seem to be aimed at someone in a different class, probably a Calculus 1 class of some kind. However, these questions came from MTH 174 Calculus 2 Test 2.
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So again I know these questions may be general knowledge questions but they really seem out of place for this test and just need to know if we're responsible for these questions if they should show up on the MTH 174 Test 2? I was going to take the test today but I didn't realize the campus is closed until this morning. Hopefully you can get this back to me before tomorrow afternoon.
You are correct that I answered for Mth 173. Since the questions were relevant to Mth 173 test 2, I just didn't stop to think about which course you are in.
I don't think any of those questions are relevant to your test. Just prepare everything in the required assignments. I'll omit anything that isn't appropriate (unless you happen to answer correctly, in which case it's only fair for me to count it).
#$&*