Need help understanding: Upperbound must be as small as possible.?
407405
Consider the point with the smallest number of neighbors, say k.  You can disconnect this point from the graph in k moves by choosing each of its neighbors in turn.\n\nIn a graph of n points and 100 edges, the point with the smallest number of neighbors can have no more than:\n\nk = Floor(200 / n)\n\nneighbors.
580938
All you have to do is find one that is either\na) larger than .5 or\nb) smaller than .45\n.501 > .500\nHence, your answer is .501
740420
Wait a minute everybody!\nthose vertical lines,( lyl ) could mean absolute value!!\nHelloooo?\nso the answerSSS could be 9 and -9\nsheesh!
48418
I think your answer is here:\nhttp://help.yahoo.com/help/us/ysearch/basics/basics-25.html
216441
Is it supposed to be less than or equal to?  Because if it's only less than, then technically it's an open interval.  That is, x can be all the infintely small points leading up to A or B, but the actual A or B is not included.\n\nAssuming that is what you meant, split it into 2 inequalities and solve each\n\n2x+6 <= x+6 ; x+6 <=3x+9\nx<=0 ; 2x>=-3 or x>=-3/2\n\nTry drawing it on a number line and see where they intersect\n\n<...-2...-3/2...-1...0...1...2... > x is everything above -3/2 and below 0, the lines would overlap, so the interval would be [-3/2,0]
65826
one sided only has the upper limit and anything below/lower limit and anything above\n\n2 sided gives both the upper and lower range for the value to fall in between
824167
The radius is actually 2/3 of the altitude.  Try that
286716
divide it by as much as you like ... let's say you can make it yield to infinitely small.\nthink of it this way : why should there be a "limit"?
981709
To extend the above two discussions and bring the matter to a conclusion, more or less.\n\nLet us define a sequence by T0 = 1, Tn = x^Tn-1.  Call the limit of this sequence as n -> infinity  as f(x).\n\nFor any given y = f(x), we see that:\n\n     lim Tn = lim Tn-1 = y\n>>\n    lim Tn = lim(x^Tn-1)=x^limTn-1\n>>\n     y = x^y\n>> \n    x = y ^ (1/y)\n\nFor y >= 1:\nThis can easily be seen to satisfy the  special cases of y = 1, 2 and 4.\n\nx, as a function of y has a maximum at y = e.~ 2.718, which leads to x~1.447.\n\nFor values of  x > e^(1/e),  f(x) does not exist; and the sequence T cannot have a limit > e.\n\nFor y < 1, we can similarly see that limits < 1/e are not possible.  The smallest x for which the limit exists is (1/e)^e ~ 0.066, giving a limit 1/e ~ 0.368
867867
Ignore the relative maximum from -2<x<3. The horizontal asymtote is defined to be the limit as x approaches infinity of the function. Which as you have calculated is 3.
925132
TimGNO is correct, although a pedant would point out that he hasn't shown this point is a maximum.  But  it is common sense.  See my response to the second time you asked the question, I got the same answer (foolishly mucking around with tangents), but make a couple of other observations you may wish to look at.
738432
the larger the number is on top, the larger the fraction.\n\nhowever, as the number on teh bottom gets larger, the value of the fraction actually gets smaller. ex: 1/2 > 1/3 > 1/4
710109
in small quanitys it is fine but not in large quanitys. Like 1ml is bad
248915
The limit as sky goes to zero from the positive direction would be ground.\nLim    = ground\nsky-->0+\n\nThe limit as sky goes to zero from the negative direction is space.\nLim    = space\nsky-->0-\n\nSince the limit from the + site does not equal the limit from the - side, the limit does not exist.
760434
impossible\n\nbut u can reduce it
731779
as little as possible.
68097
do you mean things as far as max and mins, asymptotes and things like that?\n\nif you are a little more specific i can help you better, or e-mail me, it would be a little easier  matttlocke@yahoo.com