Find a transformation
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- Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forwardEvaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0, 1), (0, 2), (2,0), and (1,0) by a suitable change of variables.arrow_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_forwardcan you answer?arrow_forwardEvaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forward
- Let 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_forwardUse the cross product to find the area of the portion of the plane defined by z = x + y which lies above the square [0, 1] x [0, 1] in the xy-plane. Draw a picture.arrow_forward
- let T(x,y) = (2x-y, xy) a) What is T(0,0) ? b) Is T a linear transformation? Explain c) Find the image under T of the region R bounded y=1/x ; y=2/x ; y= 2x; y=2x-1 d) ∫∫ R ( 2x+y/xy)dA where R is the same as in part (c)arrow_forwardSketch the surface of f(x,y)arrow_forwardFind the image of the rectangular region in the z − plane formed by joining the points0, 0 , 2, 0 , 2, 1 , (0, 1) in the w − plane under the transformation,w = (1 +i )z − 2iInterpret both the regions graphically.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage