Finding unit tangent vectors

[jwpaine]

The web homework is not accepting my answer for this, even though I've done it like the others. Have I made a mistake?

given r(t) = (t^2, t^3), find the unit tangent vector at T(t) at t = 1:

r(t) = t^2i + t^3j

T(t) = (t^2i + t^3j) / sqrt ( t^4 + t^6)
T(1) = ( i + j) / sqrt(2)

Thus: T(1) = <sqrt(2)/2 , sqrt(2)/2>

Yes, no?

 

[Unco]

If r(t) is the position vector, then the unit tangent vector is \(\displaystyle \frac{r'(t)}{||r'(t)||}\).