MAC 2313 Midterm: MAC 2313 FIU Exam 315fk
15 Feb 2019
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Prof. s. hudson: find the absolute max of f (x, y) = x(y + 1) on the closed triangular region r with vertices a(0, 0), b(0, 5) and c(5, 0). Hint: it does not occur on either the x-axis or the y-axis. Compute the area of this surface using an iterated double integral in polar coordinates: [10 points each] in each part, nd the missing limits of integration (rewrite the integral, larger, and ll in the limits). You do not have to compute the integrals. f (x, y) dx dy. 0 f (x, y) dy dx = r . 4b) r rr f (r, ) da = r f (r, )r dr d ), where r is the region inside r = 4 sin( ) and outside r = 2. Hints (but you may not need both of these): sin(5 /6) = 1/2 and sin(3 /4) = 1/ 2.
