Find the unit tangent vector at the point with the given value of the parameter .

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Find the unit tangent vector T(t)\mathbf{T}(t) at the point with the given value of the parameter tt. r(t)=⟨t2−2t,1+3t,13t3+12t2⟩,t=2\mathbf{r}(t) = \langle t^2 - 2t, 1 + 3t, \frac{1}{3}t^3 + \frac{1}{2}t^2 \rangle, t = 2

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