Find a transformation
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- Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the lines y = 3x, y = 3x+2, y = 1−x, y = 4−x.arrow_forwardPlz answer correctly asaparrow_forwardEvaluate 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_forward
- Let 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_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_forwardUse the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first quadrant that is enclosed by the hyperbolas x2 y² = 1, x² – y² = 4 and the circles x² + y? = 4 and x? + y? = 9.arrow_forward
- can 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_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_forward
- Sketch a diagram of the linear map G that maps the rectangle R = [0, 1]×[0, 1] inthe uv-plane to the parallelogram P in the xy-plane with vertices (0, 0),(2, 2),(1, 4),and (3, 6). Draw the rectangle in the uv-plane on the left and its image P in thexy-plane on the right, with an arrow labeled G in the middle. Find the map G(u, v) = (x(u, v), y(u, v)) explicitly. Set up, but do not evaluate an integral in u and v to calculate Z ZRxy dA.arrow_forwardPls help ASAParrow_forwardlet 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_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage