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Math Help - Real-valued function of closed interval

  1. #1
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    Real-valued function of closed interval

    Hi,

    Sorry the title for this post should be: Real-valued function ON closed interval.

    I am preparing to take the GRE subject test in math, and i am studying with a practice exam now. http://www.ets.org/Media/Tests/GRE/p...ctice_book.pdf. I am having a problem understanding #15. I have checked the answer, i had chosen D and it should be E.
    I guess i have two questions:

    1) Why is answer D always true. Does it just mean that the integral always exists, and because it always exists you can divide it by 5 to get M?

    2) What does the limit in answer E mean? To me basically it reduces to 0/0 at the limit which i know doesn't exist, but if it is a limit h never reaches zero, so it should exist, right?

    Hmm, thanks for any help with this.
    Last edited by Jefferythewind; September 9th 2009 at 11:37 AM. Reason: Typo
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  2. #2
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    Part D is simply the mean value theorem for integrals as 5=3-(-2)... not too sure about E
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  3. #3
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    Thanks artvandalay11, i guess i should have known that. That helps a lot. I guess on these problems if you know 4 out of the 5 answers are not the right one, then you can get it right, i am still curious about that limit.
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