Please solve this question and show all steps

(1) Evaluate the improper integral [1 ln$ d 0 x/E\" (2) Let a > b > 0 be constants and let R be the region in the rst quadrant between y = $2 and y = 52. after explaining why it is improper. Determine the volume of the solid generated by rotating R about the line a: = a. (3) Use the method of Lagrange to determine the p0int(s) on the cone y2 = 332 + 22 closest to the point (2, 0, 1). (4) Let D be the region in the rst quadrant that is bounded by the curves y = 2 + 355 and y = 53:2. Find the intersection of the curves and sketch D. Determine the volume and surface area of the solid obtained by rotating D about the :1: axis. 2 (5) Find the value of z for which the tangent plane to the surface 1'3 + 94: 22 = 1 at a point ($0,310, 20) passes through the zaxis