For the mapping u = ex cos y, v = ex sin y from the xy-plane to the MV-plane, carry out the following steps:
a) Evaluate the Jacobian determinant at (1, 0).
b) Show that the square Rxy: 0.9 ≤ x ≤ 1.1, −0.1 ≤ y ≤ 0.1 corresponds to the region Ruv bounded by arcs of the circles u2 + v2 = e1.8, u2 + v2 = e22 and the rays v = ±(tan 0.1) u, u ≥ 0, and find the ratio of the area of Ruv to that of Rxy. Compare with the result of (a).
c) Obtain the approximating linear mapping at (1, 0) and find the region R′uv corresponding to the square Rxy of part (b) under this linear mapping. Find the ratio of the area of R′uv to that of Rxy and compare with the results of parts (a) and (b).
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.