Suppose is continuous and that . Is it always true that

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- Apr 16th 2010, 01:12 PMdavidmccormickFlat tail?
Suppose is continuous and that . Is it always true that

- Apr 16th 2010, 01:17 PMDrexel28
- Apr 16th 2010, 02:56 PMLaurent
What do you mean?

In general, functions such that are not non-increasing. Some of them converge to 0, others don't.

Here's an example. Let me describe the graph of . It consists of triangular peaks that get thinner and higher : around , we put a triangular peak of width and height . (Is it clear?)

The area of the triangle at is . Since , the total area under the curve is finite, i.e. . However, clearly does not converge to 0. We even have for . - Apr 16th 2010, 03:00 PMDrexel28