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(1) Compute the Jacobian for the following functions f R2 R2: (a) 2u 3v 5u 8v y(u, v) (2) y(u, v) u v (3) u cos 0 v sin 69 y(u, 0) u sin 0 v cos 0 (4) eu sin 0 r(u, 0) eu cos 0 y(u,0) (5) Compute the following integral using polar coordinates: dA r where R is the region determined by a circle of radius one with center at (0,0)
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