something not to do....

Here's a logic I'm seeing on the test, in fact I've seen it on a lot of tests for a lot of years:

r(t)=<t,t^2,t^3/3>

so

r'(t)=<1,2t,t^2>   evaluated at t=0 gives

1+0+0 so

r'(0)=1,

right?

WRONG!

<strong emphasis>DO NOT DO THIS</strong emphasis>

evaluating a vector function at a given time does NOT mean that you get to add all the components. The correct answer is r'(0)=<1,0,0>.  You have to substitute t=0 in every component, the fact that evaluating the component gives that the component is equal to 0 does not mean that the component disappears.  It is still there being zero.