Find a transformation
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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_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_forwardConsider 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_forward
- Which of the following integral is the integral S SR elzi9)/= )dA where R is the trapezoidal region with vertices (1,0), (2,0), (0,-2) and (0,-1), by changing variables of the integral by using the transformation u=x+y and v=x-y. O a. S", eu/"dudv dudu 2 O . " e/"dudv O d. f fo dudu O e. f S",dudv 2arrow_forwardFind the global min and max of the provided function on the provided region R: f(x,y) = x - y - xy on the triangle R with vertices (0,0), (0,2), and (4,0)arrow_forwardLet G(u, v) = (2u + v, 5u + 11v) be a map from the uv-plane to the xy-plane. Find the image of the line v = 4u under G in slope-intercept form. (Use symbolic notation and fractions where needed.) y =arrow_forward
- Find 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_forwardIdentify all extrema of the function f(x,y)=x³+y³-3x-12y +20 on the plane and characterize them.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