Please read all of the following rules carefully before proceeding: check that this exam contains 11 pages, unless otherwise instructed, please clearly indicate all work involved in the solution of each problem. 2x + 1 x2 7x + 12 dx. Use the symbols + and whenever appropriate. If a limit does not exist, state why. 3. tan2 x + 2x x2 + x lim x 0 lim x (xe1/x x) ex + 1 x2 lim x 0. A region enclosed by y = sin x and y = 0 for 0 x is rotated about x = /2. Sketch the region being rotated, with the coordinate axes and the axis of rotation to support your answer. All the materials required to build a pyramid are located at ground-level. The pyramid is built by laying a foundation and lifting material from the ground onto the part already erected. Let (measured in kg/m3) be the density of the material.
