MAC 2313 Midterm: MAC 2313 FIU Exam 215k
15 Feb 2019
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Prof. s. hudson: [10 pts] evaluate the integral: r 2. 0 he3t, sin( t/2)i dt: [10 pts] find the equation of the osculating plane for the curve cos(t)i + sin(t)j + k at t = /4. Explain your method brie y and circle your answer: [10 pts] a particle moves along a curve with speed ||v|| = t2 + e 3t. Find the scalar tangential component of acceleration when t = 0: [10 pts] evaluate the limit (if it exists) as (x, y) (0, 0) by converting to polar coordi- nates, lim px2 + y2 ln(x2 + y2). Remember to show all your work: [15 pts] let f (x, y, z) = 2xy2z3, p (1, 1, 2) and q(0. 99, 1. 02, 2. 02). 5 j: [15 pts] answer t or f; you do not have to justify your answers (but this sometimes helps, if there is some minor misunderstanding):
