Consider the following vector function. r(t) = ⟨t2 − 2t, 1 + 3t, 13 t3

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Consider the following vector function. r(t) = ⟨t2 − 2t, 1 + 3t, 13 t3 + 12 t2⟩ Find each of the following. r′(t) = r′(2) = |r′(2)| = Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = ⟨t2 − 2t, 1 + 3t, 13 t3 + 12 t2⟩, t = 2 T(2) =

Consider the following vector function. r(t) = ⟨t2 − 2t, 1 + 3t, 13 t3 + 12 t2⟩ Find each of the following. r′(t) = r′(2) = |r′(2)| = Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) = ⟨t2 − 2t, 1 + 3t, 13 t3 + 12 t2⟩, t = 2 T(2) =

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Consider the following vector function.

r (t) = ⟨ t^{2} - 2 t, 1 + 3 t, \frac{1}{3} t^{3} + \frac{1}{2} t^{2} ⟩

Find each of the following.

\begin{aligned} r^{'} (t) & = ◻ \\ r^{'} (2) & = ◻ \\ | r^{'} (2) | & = ◻ \end{aligned}

Find the unit tangent vector

T (t)

at the point with the given value of the parameter

t

.

\begin{array}{l} r (t) = ⟨ t^{2} - 2 t, 1 + 3 t, \frac{1}{3} t^{3} + \frac{1}{2} t^{2} ⟩, t = 2 \\ T (2) = ◻ \end{array}

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