Suppose you start at the point (0,0,3) and move five units along the curve x=3sint, y=4t, z=3cost in the position direction. Where are you now?

Answer 1

Put t=5
then
(0.26, 20, 2.98)

Answer 2

=(3sin1,4,3cos1)

Answer 3

Arclength is given by R0k |r 0(t)|dt, and in this case |r 0(t)| = 5, so we want to
find the k such that this integral is equal to 5, i.e., R0k 5dt = 5k, so k = 1. Thus we have
traveled 5 units along the curve when t = k = 1, so we’re at (3 sin 1, 4, 3 cos 1).

Answer 4

Arclength is given by R0k |r 0(t)|dt, and in this case |r 0(t)| = 5, so we want to
find the k such that this integral is equal to 5, i.e., R0k 5dt = 5k, so k = 1. Thus we have
traveled 5 units along the curve when t = k = 1, so we’re at (3 sin 1, 4, 3 cos 1).(R0k=integration from 0 to k)