1. Be sure to look over practice exam 1, 2 and 3 to review that material. 11] 2. If w'[t} = is the rate of growth of a child in pounds per year, nd f w'qjt} cit and give an 5 interpretation of your answer. 3. Evaluate the following denite and indenite integrals: "f4 1 + cos? {3) (a) f cnazm \"'5 (a) L slum-"ca (C) f(1+r)2dr {a} [113 '9'} Line-4F 1 En: (f) L 1 + E25 :13 4. Sketch the region hounded by y = 1.33 1 and w y = 1. Then nd the area. of the region. 5. Use calculus to nd the area of the triangle with the gimn vertices. {Gilli} (3,1) {112) 1 '5. Consider the graph of the curve 3; = -. z {a} Find the area under the curve from E = 1 to E = l. (b) What happens to the area under the curve as the right hand endpoint goes to 00'? (c) Find the volume of the solid obtained by rotating this curve around the maxis from m = 1 to z = l. (d) What happens to the volume in part [c] as the right hand endpoint goes to co? (e) Find the 1wolunie of the solid whose base is this region bounded by the curves 3; = 13's, y = G, :r = 1 and z = lllll and whose crosssections perpendicular to the zaxis are right triangles whose height is half their base. {1"} What happens to the volume in part (e) as the right hand endpoint goes to DO? 7. Consider the region bounded by y = ,y = 1 and z = 4. Setup, but do not evaluate, integrals to nd the following: {a} Area of region {b} Volume of solid obtained by rotating the region around the :rasis. {c} Volume of solid obtained by rotating the region around the yaxis. {d} Volume of solid obtained by rotating the region around the line y = 1. (e) Volume of solid obtained by rotating the region around the line a: = 5