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)=⟨tan⁡−1t,2e2t,8tet⟩,t=0\mathbf{r}(t) = \langle \tan^{-1} t, 2e^{2t}, 8te^t \rangle, t = 0

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