61. 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. 1 (b) Let G = F¬1, Show that |Jac(G)| = 2|v| (c) Apply the Change of Variables Formula to prove the formula 3 r² $(v)dv Sl C) dz dy = 1/2 ye/x ·dx dy. (d) Apply (c) to evaluate

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A: Given a curve C is a parabola from (0, 0) to (2, 4)

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A:

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A:

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A:

Q: 2. Given f (x, y) = x + 2y, find F(x, y) =Vf and sketch it along with the contour map of f.

A:

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A: Given that the function is                       f(x, y, z)=3x2+3y2+3z2.