B. [4 pts] Suppose that r '(t) = (2t, 4 cos(2t), 2et/2 ) . If r (0) = (3,0,2), calculate r (t). A T(t) = (t2 + 3, -4 sin(2t), 2et/2 B r (t) = +2 + 3, -4 sin(2t), 2et/2 + 2 C T (t) = (+2 + 3, 2 sin(2t), 4e*/2 + 2) D r(t) = (t2 + 3, 2 sin(2t), 4et/2 - 2) E r (t) = (t2 + 3, -8 sin(2t), et/2 + 2) F None of these Explanation:C. [4 pts] A curve is parameterized by the vector-valued function ?(t) = (101/5 + 4t,4t + 5, 3). Find a paremeterization of the tangent line to the curve at (any, 2) - (50,25, 3). in) = (4t + 50,4t+ 25,3) 3(3) = (t + 50, 4: + 25, 3) 3a) = There is no such tangent line since the curve doesn't pass through (5D, 25, 3). None of these. Explanation: D. [4 pts] If the lines 61 and 42 are parameterized by (4t, 2t + 2, 3t + 1) and (2t, t + 2, 3t - 2), then &1 and &2 are actually the same line. B are parallel, nonintersecting lines. C intersect at one point in the xyz-plane. intersect at more than one, but finitely many, points in the ryz-plane. E are skew lines. Explanation