Vector-valued functions

• Oct 28th 2013, 10:39 AM
Vector-valued functions
Attachment 29606Attachment 29606Hi 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
• Oct 29th 2013, 12:25 AM
chiro
Re: Vector-valued functions

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.
• Oct 29th 2013, 02:14 AM