# Thread: Real-valued function of closed interval

1. ## 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.

2. Part D is simply the mean value theorem for integrals as 5=3-(-2)... not too sure about E

3. 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.