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bloodhound

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Posts posted by bloodhound

  1. Well... yea... i am back. Done me exams. One of the modules was a bitch, and it dragged my average down. hovering around 70% at the moment. Didn't really put much effort into it. I normally start revising the night before the exam which has generaly been my style and has got me through so far. don't know if I should change it. But with 6 exams with 4 in 4days maybe i took a toll. Well anyway I am starving as usual. Hopefully I will start posting again. So... yea... how's everyone been doing?

  2. The columns of [math]A[/math] span [math]\mathbb{R} ^3[/math'] if and only if they are linearly independent.

    Hmm... I am not sure about that... I think it spans iff every element of R^3 can be written as a linear combination of the column vectors. A set of vectors which span a space and on top of that are linearly independent is the basis set.

  3. Just general info:

     

    A point of inflection is a point where a curve crosses its tangent. So a point of inflection doesnt have to be a stationary point. But a stationary point which is neither a maximum or a minimum has to be by default a point of inflection.

     

    For the case where the second derivative is equal to 0 at the stationary point, one of the ways forward is to look at the power series (taylor series) of the function and how it behaves close to the stationary point.

  4. i assume you meant [sinx][exp(-sinx)]. just do the most obvious thing which is to find its derivative.

     

    which comes out to be

     

    [cosx]exp[-sinx] - [sinx][cosx]exp[-sinx]. to find the stationary points , find points such that the derivative at the point is zero. so setting that to 0 we get

     

    [cosx]exp[-sinx] - [sinx][cosx]exp[-sinx] = 0

     

    iff cosx - sinx[cosx] = 0 as the exponential is never 0.

     

    so we have either cosx = 0 or sinx = 1

     

    which gives just the same arithmetic sequence of solutions namely

     

    (pi/2 + n*pi), where n ranges over the integers.

  5. well, the first flaw lies in you taking squares.

     

    you have written[math]e^{(i\pi)^{2}}[/math] , when it should be

    [math](e^{i\pi})^2[/math]

    but then, you might say

     

    [math](e^{i\pi})^{2}=1[/math]

    [math](e^{2i\pi})=1[/math]

    [math]2i\pi = \ln(1) = 0[/math] and how does that work?

     

    its just like dave said, taking logarithms of complex numbers is a dodgy proposition. Lets just say it is not always true that [math]\ln{e^{z}}=z[/math] if you are working with complex variables.

     

    [edit] why isn't the latex showing up?[/edit]

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