Question

1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz dV, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 1), (0, 1, 1), and (0, 0, 1). » 6. Determine whether.ornot F is a conservative vector field. If it is, find a function f such that F-vf. - F(x, y) = (In y +x) l + (inx+-)j 7. A region in the xy - plane is given. Find equations for a transformation T that maps a rectangular region S in the ux - plane onto R, where the sides of S are parallel to the u- and v- axes. R is bounded by y-2x-1, y-2x + 1, y 1-x, and y 3-x- 8. Use Green's Theorem to evaluate the line integral along the given positively oriented curve. » dx + (2x + cos y2) dy, where C is the boundary of the region enclosed by the parabolas y-x2 and x-y2. , 9. Evaluate the line integral c 2y dx + (1 -x) dy, where C is a portion of y -1- x3 from 110. Evaluate IIE yx2 + Уг + z2 dV, where E lies above the cone z-yx 2 + y2 and between spheres x2 + y2 + z2-1 and x2 + y2 + z2-4. »

All of 10 questions, please.

Answer 1

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