Question

r(t) = . Find ds/dt

Answer 1

\[r(t)=<x,y,z>=<\cos{\pi t},\sin{\pi t},3t>\]\[\frac{ds}{dt}=\sqrt{(x')^2+(y')^2+(z')^2}=\]\[=\sqrt{(-\pi\sin{\pi t})^2+(\pi\cos{\pi t})^2+3^2}=\sqrt{\pi^2+9}\]