Sketch the region D bounded by the curves y = 2/x, y = 1
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Sketch the region D bounded by the curves y = 2/x, y = 1/(2x), y = 2x, y = x/2 in the first quadrant. Let F be the map u
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Sketch the region D bounded by the curves y = 2/x, y = 1/(2x), y = 2x, y = x/2 in the first quadrant. Let F be the map u = xy, v = y/x from the xy-plane to the uv-plane. (a) Find the image of D under F. (b) Let = F ?1. Show that |Jac()| = 1 2|v| . (c) Apply the Change of Variables Formula to prove the formula D f y x dx dy = 3 4 2 1/2 f (v) dv v (d) Apply (c) to evaluate D yey/x x dx dy.
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