MATH 126 Midterm: MATH 126 UW Midterm 2 Fall 16taggartExIIans

(1) Find the shortest distance from the surface x2 + yz + 2z = 10 to the origin. Also identify the point that is closest to the origin. 2) Compute £52 ez? dxdy (3) Compute JJp (zy + 2) dA where D is the triangle with vertices (-1,0), (-1,-1). and the origin. (4) Set up an integral (but don't evaluate) to compute the volume of the solid that lies below the surface given by z = 4x+20 and lies above the region in the ry-plane bounded by y = x2 and y = 8-x2 (5) Evaluate ffhe r dV where W is the region bounded by y = x2, y = x, z = 0, and 2x + z = 4 (6) Compute ID ry dA where D is the region bounded by x 뇻 0, y 0,22+92 = 1, and x2 + y2 = 9.