MATH 221 Midterm: MATH221 CofC math221sp05
15 Feb 2019
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No calculators, notes, books, or any other outside materials. Supporting work will be required on every problem (unless otherwise indicated). You are expected to know the values of all trigonometric functions at multiples of /4 and of /6. Let r be the rectangle [1, 3] [ 1, 3] in the xy-plane, and let f (x, y) = x + 3y. Find a riemann sum for f (x, y) on r using n = m = 2 and choosing the sample points to be the point in each subrectangle that is closest to the origin. Find the equation of the plane tangent to the surface 16 x y2z = 23 at the point (4, 3, 1). Evaluate the line integral !c(y 2) dx + (x 2) dy where. C is the closed path pictured at right. (each arc in c is a semicircle. ) Let b be the region {(x, y, z) ir3 : 1 x2 + y2 + z2 9}.
