Recent content by Logik

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    Prove that f(n) = n * log (n) is O(n(1+sqrt(n))).

    I don't know where to start to solve for c.. that is my problem... I don't understand where the 1 comes from... I know O(logn) < O(sqrt(n)) so I can get that but where is the (1+srt(n)) comes from?
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    Prove that f(n) = n * log (n) is O(n(1+sqrt(n))).

    yes well I don't know how to go from f(n) to g(n)... the examples I have seen were just that you would multiply so part of f(n) until you could group everything together to get c* g(n) but this time I don't see how I can multiply anything to get anything that looks like g(n)...
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    Prove that f(n) = n * log (n) is O(n(1+sqrt(n))).

    f(n) is O(g(n)) if and only if there exists an n_0 part of natural numbers and a constant C that is part of rational numbers for which f(n) <= that c*g(n) for all n >= n_o I know the def just don't know how to get g(n)...
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    Prove that f(n) = n * log (n) is O(n(1+sqrt(n))).

    Homework Statement Prove that f(n) = n * log (n) is O(n(1+sqrt(n))). Homework Equations n/a The Attempt at a Solution I really don't know what to do else I wouldn't be here :? Some hints would be appreciated!
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    Vector field

    TO DICK. F=(x*i, y*j) DIV F = d/dx(x) + d/dy(y) = 2 which means it goes outward and not to the origin... // EDIT F=-(x^2 + y^2)^3/2 * (x*i, y*j)
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    Vector field

    F=k*(x^3*i,y^3*j), k<0 ? Is this good then? // I did not mean inversely.
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    Vector field

    Homework Statement A particle is attracted toward the origin by a force proportional to the cube of it's distance from the origin. (...) What would be this Force equal to (in xy plane)? The Attempt at a Solution So distance is Sqrt[x^2+y^2]... and from here I don't know what to...
  8. L

    Nonlinear ODE

    wow I'm so stupid... dy/dt = y^(1/2) dy/y^(1/2) = dt 2y^(1/2) = t + c y^(1/2) = 2t + 2c y = 4t^2 + 8tc + c^2 thanks
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    Nonlinear ODE

    Homework Statement I have to find the solution of (1) and show that it is not unique if y(0) = 0. I can prove it is not unique by using Picard's theorem but I don't know how to find the non trivial solution. Homework Equations (1) y(t)' = Sqrt(y(t)) The Attempt at a Solution I...
  10. L

    Complex derivatives

    e^ix first i*e^ix second i^2*e^ix e^-ix first -i*e^-ix second i^2*e^-ix p.s. I've read about the Cauchy-Riemann equation but just not sure how to apply it... should I split the exponential in a sin and a cos? p.s.s. There are probably rules, like exponential function are always derivable or...
  11. L

    Complex derivatives

    I have to solve an ODE with variation of coefficient technique. It's pretty easy but I have no clue what is the first and second derivative of e^ix and e^-ix.
  12. L

    Weighted lest square fit

    pdf PDF of latex file.
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    Weighted lest square fit

    Homework Statement I have a project for one of my class and I have been given a sheet to do the statistical analyst of my data. I am not convince this sheet is proper and I need someone to look over it it. I don't understand where my Delta R goes... Homework Equations \chi^2...
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    Number if rational iff it has periodic decimal expansion

    Thanks... that was kinda easy but I guess you just need to know it. Btw good job, this forum is a great ressource :P
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    Number if rational iff it has periodic decimal expansion

    Ok well I guess my intuition was bad. I made a few search on books.google.com and found a couple of proofs. One is pretty easy and I actually though of that solutions before but didn't know how to generalise it. My only problem now is that I'm not familiar with one notation in the proofs. I...
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