MATH 231 Final: MATH 231 Spring 2017 Final Exam
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Instructions: please, write your solutions clearly and completely. Answers without work will be given no credit. Please turn o all phones and remove any smartwatches. 3 i from the origin to the point: 18, 12, 9, 21. Spring 2017: (5 points) a moving particle starts at an initial position r(0) = h3, 0, 1i and its velocity is v(t) = hcos(2t), 3t2, sin ti. Find the acceleration of the particle at the point (3, 3, 3): 6 j k, 6 j, 2i + 6 j + k, 2i + 6 j k, (5 points) evaluate lim (x,y) (0,0) x2y2 x4 + y4, 1. B: the limit does not exist, 0. Math 231 - final exam - b: (5 points) suppose z is implicitly de ned by xy2 + yz3 = z2. X (0, 1, 1): 0, 2, 1, 1, (5 points) at the point (1, 1, 0), calculate the directional derivative of f (x, y, z) = x2y cos(z)
