Find a transformation
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CALCULUS EARLY TRANSCENDENTALS W/ WILE
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- 9. Let R be a square with vertices (0,0), (1,1), (2,0) and (1, -1) in the xy-plane. It might be useful/helpful to sketch the region R and the region S a) Find the image Sin the uv-plane under the transformation T: x=u + v, y = u - V hint: solve for u by solving for x + y (use system) b)Write the Jacobian Matrix of partial derivatives c) evaluate the determinant of the Jacobian d) Rewrite the integral using a change of variables to u and v with the Jacobian and evaluate the new integral. SSR xydAarrow_forwardLet B be the region in the first quadrant of the ry-plane bounded by the lines r+y = 1, r + y = 2, (x – y)? I = 0 and y = 0. Evaluate -drdy by applying the transformation u = r+ y, v = x – y 1+x + y Barrow_forwardLet D be the triangular region in the uv-plane with vertices (0, 1), (4, 1), (1, 3) and letG(u, v) = (u − v, 2v).Sketch D in the uv-plane and G(D) in the xy-plane.Find the area of G(D) by using Jac(G)arrow_forward
- Consider the transformation x =r cos 0, y=r sin 0, z = z from cylinderical to rectangular coordinates, a(x, y, z) a(r, 0, z) * where r > 0. Find 1 -rarrow_forwardLet G(u, v) = (5u + 2v, 5u + 9v) be a map from the uv-plane to the xy-plane. Calculate Jac(G) = d(x,y) a(u,v)* (Use decimal notation. Give your answer as a whole number.) Jac(G) =arrow_forwardPlz don't use chat gpt, don't copy pastearrow_forward
- Identify the notation that shows the transformation of triangle SML onto triangle S'M'L' to show the figures are similar. Y M. O x, )(x+6, y-6) O xy)→(v, x) O X,y)(x+2, y-2) Oxy)→(x+1, y-1)arrow_forwardFind the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2, y = 0, and y = 3x in the xy-plane.arrow_forwardaz. Suppose F = (2xz + 3y²) a, + (4yz²) a;. (a) Calculate S[F·dS, where S is the shaded surface in Figure 1. (c) Based on your results for parts (a) and (b), what named theorem do you think is being satisfied here, if any? (b) Calculate SF· dl, where C is the A → B → C → D → A closed path in Figure 1. az C C (0,1,1) D (0,0,0) (A ay В ax Figure 1: Figure for Problem 1.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage