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Please help me with this Math question.

 
Old 10-06-2010 at 09:39 PM   #1
ruby101
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Please help me with this Math question.
I have midterm 1A03 tmr. Can someone here help me with this question : Is M3 always a better estimate for a continuous function than L3? If not, give an example of a continuous function such that L3 is closer to the actual value of [int from 3 to 6] f(x)dx than M3. Thanks in advance !
Old 10-06-2010 at 10:02 PM   #2
britb
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There's this site called Avenue...
Old 10-06-2010 at 10:04 PM   #3
Lessica
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MATH 1A03 isn't on Avenue.
Old 10-06-2010 at 10:12 PM   #4
Lessica
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Also (and don't hold me to this, because I'm not sure either), you need a function that increases AND decreases on the interval; if it only does one or the other, using the left endpoints will underestimate or overestimate the area.
I think one example that works is sin(x), though that may not always be the case, depending on the interval.
If you're allowed to draw the function instead of naming it, it's a lot easier.

ruby101 says thanks to Lessica for this post.
Old 10-06-2010 at 10:16 PM   #5
ruby101
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yeah, it 's a lot easier if i can draw the function only so according to the question do u think i have to name the function ?
Old 10-06-2010 at 10:37 PM   #6
Lessica
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I really can't say; you'd have to find Haskell during her office hours and ask her. Personally, I think it's unlikely we'll get the same questions on our midterm, so it shouldn't matter too much.
Old 10-06-2010 at 10:43 PM   #7
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ok, aw thanks
Old 10-07-2010 at 03:04 AM   #8
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Hint: Suppose I have a function f(x), for which midpoints yield a better approximation than left endpoints. (This should be fairly easy to find) Now, what happens if I 'shift' my function by half the interval length, (delta)x/2?

e.g. in this case, (delta)x = 1 (since we're making 3 divisions from 3 to 6), so if I shift my function to the right by 1/2...what happens to my midpoints vs. my left endpoints? Set g(x) = f(x - 1/2).

Last edited by Mowicz : 10-07-2010 at 03:07 AM.



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