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Find the a ea of the parallelog -a 1 wi •I : . Sketch the region ofintegration_.. 6 y f{x1 y) dxdy 0 0 - y (6, 6} • (0,6) (0,6) y=x y=x (6,0) x Change the order of integration. to F(X, y) dy dx Find the volume of the given solid. Under the plane 9x + 2y - Z = 0 and above the region enclosed by the parabolas y - x2 and x = y2 Evaluate the double integral. 110 (9x - 8y) dA, D is bounded by the circle with center the origin and radius 3 Consider the points below. P(1, 0, 1), Q(-2,1,3), R(4,2,5) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR. a) Find parametric equations for the line through (3, 4, 4) that is perpendicular to the plane x - y + 2z=5. (Use the parameter t.) (x(t), y(t), z(t)) = ) (b) In what points does this line intersect the coordinate planes? xy-plane (x, y, z) = ( ) yz-plane (X, y, z) = ( ) xz-plane (X, y, z) = ( )

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