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Math Help - Vector-valued functions

  1. #1
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    Vector-valued functions

    Tut4.pdfTut4.pdfHi i have spent a huge amount of time at these maths in the attached file, i was wondering if someone could help me out with mostly 3 but also 2 . Cheers

    For q2 i get as far as:

    S=L=integral of 0 to t , sqrt((12/t^2 + (sint)^2+(cost+tcost-sint)^2 but dont know where to go from here

    For q3: i get T(t) but it is seriously complicated so when i go get T'(t) it gets even worse differentiation and it looks horribly wrong

    Anyhelp in the right direction is greatly appreciated,
    Regards,
    Conor
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  2. #2
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    Re: Vector-valued functions

    Hey bradyc12.

    For Q2 you have to use the parameterization where ds^2 = dx^2 + dy^2 + dz^2. Now divide by dt^2 and take a square root to give you:

    (ds/dt) = SQRT((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2).

    Remember that the key thing with arc-length is that you finding infinitesimals of pythagoras' theorem where you are adding up the hypotenuses to get the final arc-length.
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  3. #3
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    Re: Vector-valued functions

    Cheers Chiro,
    Im afraid i already knew that its just when i get past using that formula the integral gets really mess and i cant get a proper answer out of it, any chance you can shine some light on that and q3 please?
    Cheers
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  4. #4
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    Re: Vector-valued functions

    Can you show us your steps and how far you got?
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