Please, could someone please help me step by step with the following problems, I've tried to work them and it's driving me nuts to rewrite everything again and then to find out that I am making the same mistakes! My main problem is being able to differentiate correctly.
1) Find the arc length of the curve on the interval (0, 2pi) of the following:
Cylcoid arch: x= a (θ - sinθ), y= a (1-cosθ)
2) Find the arc length on the curve of the given interval (1, 2) of the following:
x= t , y= t^(5) /10 + 1 /6t^(3)
3) Find dy/dx and d^(2) y / dx^(2) (first derivative and 2nd derivative), and find the slope and concavity (if possible) at the given value of the parameter of the following:
a) x= 2 + sec θ, y= 1+ 2 tan θ When θ= pi/6b) x= cos θ, y= 3 sin θ When θ= 0