00:01
In this problem, we want to sketch a given space curve by first evaluating a few points of the curve.
00:11
So we have r of t equal to t in the f component, 4t squared in the y component, and 2 thirds t cubed in the z component.
00:21
Let's evaluate r at t equal to minus 2.
00:25
Let's replace the t with minus 2, and we obtain minus 2 in the f component, 8 in the y component, and minus 16 over 3 in the z component.
00:45
Let's evaluate r at 0, and we obtain 0, 0, 0.
00:56
And lastly, let's evaluate r at i plus 2, and we obtain 2, 8, and 16 over 3.
01:09
So our curve starts at the origin, has a point right here, and we have a point at x equal to 2, y equal to 8, and z equal to 16 over 3...