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1.   Find the unit tangent vector to the curve \({\bf r}(t) = \langle 3te^t, \frac{4}{\ln 2} 2^t \rangle\) at \(t = 0\)

a.  \({\bf T}(0) = \langle 0, 1 \rangle \)

b.  \({\bf T}(0) = \langle 3, 4\rangle \)

c.  \({\bf T}(0) = \langle 0, 1\rangle \)

d.  \({\bf T}(0) = \langle \frac{3}{5}, \frac{4}{5} \rangle \)

e.  \({\bf T}(0) = \langle \frac{1}{2}, \frac{\sqrt{3}}{2}\rangle \))

2.   Find the principal unit normal vector to the curve \({\bf r}(t) = \cos(t^2), \sin(t^2) \rangle\) where \(t > 0\)?

a.  \({\bf N}(t) = \langle -\cos(t^2), -\sin(t^2)\rangle \)

b.  \({\bf N}(t) = \langle t^2\cos(t^2), t^2\sin(t^2)\rangle \)

c.  \({\bf N}(t) = \langle -t^2\sin(t^2), t^2\cos(t^2)\rangle \)

d.  \({\bf N}(t) = \langle \sin(t^2), \cos(t^2)\rangle \)

e.  \({\bf N}(t) = \langle -t^2\sin(t^2), -t^2\cos(t^2)\rangle \)

3.  Evaluate the indefinite integral. \(\int \langle t e^t, e^{-t} \rangle dt\)

a.  \(\langle \frac{1}{2}t^2 e^t + c_1, -e^{-t} + c_2 \rangle \)

b.  \(\langle \frac{1}{2}t^2 e^t + c_1, e^{-t} + c_2 \rangle \)

c.  \(\langle te^t - e^t + c_1, -e^{t} + c_2 \rangle \)

d.  \(\langle te^t + e^t + c_1, e^{-t} + c_2 \rangle \)

e.  \(\langle te^t - e^t + c_1, -e^{-t} + c_2 \rangle \)

4.  What does it mean if an object has a constant acceleration of \(\langle 0, 0\rangle \)?

a.  The object is stopped.

b.  The object is moving in a circle at constant speed.

c.  The object is moving in a straight line at constant speed or is stopped.

d.  The object is moving in a circle at constant speed or is stopped.

e.  The object is moving in a circle at constant speed or a straight line at constant speed.