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Math Help - Linear Algebra

  1. #1
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    Linear Algebra

    hey I have this question due for an assignment for uni in a couple of days, and I dont really know where to start...

    Take a function f that is infinitely differentiable at 0.\
    - find a degree 1 polynomial p1(x) = a0 + a1x such that

    p1(0) = f(0) and p1'(0) = f'(0)

    is this polynomial unique? can you find a degree 1 polynomial so p1''(0) = f''(0)?

    where do i start with this one? i just dont get the general way which to start this problem...can anyone help?...i only really want a hint on where to go with it, not the answer as well...im new here so i dont get how it all works
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  2. #2
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    possible solution

    Find a0 and a1 in terms of f(0) and f'(0).

    (you aren't studying MATH1220 by any chance are you?)

    Hoppo.
    Last edited by Hoppo; September 2nd 2008 at 05:19 AM.
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  3. #3
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    haha maybe

    you wouldnt happen to be adam with longish blonde hair that hangs with sean would you?
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  4. #4
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    I don't think so ...

    I'm trying to find help with the last bit of that question... what's an infinitely differentiable function? (e^x?)
    Last edited by Hoppo; September 2nd 2008 at 05:19 AM.
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  5. #5
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    i dont know his last name...sorry i was thinking about the wrong guy

    umm infinitely differentiably means you can take infinitely many derivatives of that function... as an example:

    y = e^x

    is infinitely diff'ble as

    y' = e^x
    y'' = e^x
    ...

    hope that explains it, im not sure how it works into that part of the question though
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  6. #6
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    but you can take infinitely many derivatives of anything can't you? Alot of functions jeventually become zero... but can't you still differentiate them?
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  7. #7
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    yeah you can, which is why you do it for the general function f, instead of picking some random function, like you did in a)

    ill give you a hint though and say look in your algebra textbook for that question

    how do you explain part b)? like any degree one function will have p''(0) = 0 always, so as long as f''(0) = 0 it will work...but how do you explain that the polynomial is unique?
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