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# Find r′(t), r(t_0), and r′(t_0) for the given value of t_0. Then sketch the plane curve represented by the vector-valued function, and sketch the vectors r(t_0) and r′(t_0). Position the vectors such that the initial point of r(t_0) is at the origin and the initial point of r′(t_0) is at the terminal point of r(t_0). What is the relationship between r′(t_0) and the curve? r(t) = ⟨e^-t, e^t⟩, t_0 = 0

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$r'(0)$ is tangent to r(0) at $t=0$

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