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Hi. Just did a show that involving an approximation and I'm not convinced that what I've done is rigorous. Could someone please check it for me?
"Let . Show that, for large positive x, ."
My method goes like this. for large positive x and so . Also for large positive x, so so . Rearranging this gives . Finally, for large positive x, so
Is this a solid argument? Thanks 92.2.16.39 ( talk) 10:09, 20 June 2009 (UTC)
You may prefer to simplify first and approximate afterwards.
Bo Jacoby ( talk) 14:37, 20 June 2009 (UTC).
Please tell me about the algorithm of finding International Roughness Index(of a road surface)from a longitudinal profile data. —Preceding unsigned comment added by 113.199.158.140 ( talk) 12:36, 20 June 2009 (UTC)
I'm a little hazy on N&S conditions so wanted to check my thoughts with people who can tell me if I'm right or wrong. Let . I have to find N&S conditions on b and c a) for f(x) to have two distinct real roots and b) for f(x) to have two distinct positive real roots.
For a) I get that just from using the fact that if the turning point is below the x axis, you've got two distinct roots.
For b) I again get , for the same reason as before. I then get c>0, which ensures that the roots are of the same sign and b>0, which says the minimum point occurs in the first quadrant (at least I think that's its name; I mean bottom right). So the y-intercept is positive, both the roots are of the same sign and the turning point is in the first quadrant, so between them, they say that the roots are distinct and positive.
Are they necessary and sufficient or not? Thanks 92.4.255.16 ( talk) 17:52, 20 June 2009 (UTC)
Has anybody already seen an optimization problem like this one:
Incidentally, I know the answer (it is hidden here in case somebody prefers not to see it), but I'd like to settle this and other similar but more difficult problems into a general theory/method, if there is any available. -- pma ( talk) 21:17, 20 June 2009 (UTC)
Mathematics desk | ||
---|---|---|
< June 19 | << May | June | Jul >> | June 21 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hi. Just did a show that involving an approximation and I'm not convinced that what I've done is rigorous. Could someone please check it for me?
"Let . Show that, for large positive x, ."
My method goes like this. for large positive x and so . Also for large positive x, so so . Rearranging this gives . Finally, for large positive x, so
Is this a solid argument? Thanks 92.2.16.39 ( talk) 10:09, 20 June 2009 (UTC)
You may prefer to simplify first and approximate afterwards.
Bo Jacoby ( talk) 14:37, 20 June 2009 (UTC).
Please tell me about the algorithm of finding International Roughness Index(of a road surface)from a longitudinal profile data. —Preceding unsigned comment added by 113.199.158.140 ( talk) 12:36, 20 June 2009 (UTC)
I'm a little hazy on N&S conditions so wanted to check my thoughts with people who can tell me if I'm right or wrong. Let . I have to find N&S conditions on b and c a) for f(x) to have two distinct real roots and b) for f(x) to have two distinct positive real roots.
For a) I get that just from using the fact that if the turning point is below the x axis, you've got two distinct roots.
For b) I again get , for the same reason as before. I then get c>0, which ensures that the roots are of the same sign and b>0, which says the minimum point occurs in the first quadrant (at least I think that's its name; I mean bottom right). So the y-intercept is positive, both the roots are of the same sign and the turning point is in the first quadrant, so between them, they say that the roots are distinct and positive.
Are they necessary and sufficient or not? Thanks 92.4.255.16 ( talk) 17:52, 20 June 2009 (UTC)
Has anybody already seen an optimization problem like this one:
Incidentally, I know the answer (it is hidden here in case somebody prefers not to see it), but I'd like to settle this and other similar but more difficult problems into a general theory/method, if there is any available. -- pma ( talk) 21:17, 20 June 2009 (UTC)