MATH 126 Midterm: MATH 126 UW Midterm 2 Fall 14perkinsExIIans
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The position of a particle is given by r(t) = 4t i + 2t2 j + ln t k. find all points. Second midterm solutions (8 points) on the path where the velocity is perpendicular to the acceleration. 1 t k r (t) = 4 i + 4t j + 1 t2 r (t) = 4 j k. 0 = 16t4 1 t = . 2 is not in the domain of the function. Thus the only point is r (cid:16) 1. Calculate the equation of the tangent plane to the hyperboloid 3x2+5y2 z2 = 8 (8 points) at the point (2, 1, 3). At the point (2, 1, 3), z is positive so we can write z = 3x2 + 5y2 8. The tangent plane is z 3 = 2(x 2) 5 or. 6x 5y 3z = 8 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(2, 1) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(2, 1) 3 (9 points) region in the rst quadrant where x + y 7.
