Summer 2017: (15 pts) the base of a solid region s is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross sections perpendicular to the y-axis are equilateral triangles. Consider an equilateral triangle with sides of length b. The angles in this triangle are all equal to 60 so that the height h of the triangle is h = b sin 60 = Thus the area of the equilateral triangle is a = 2 case here, the length of the sides of our triangles is x = 1 y so that their area is a(y) = volume of the solid is then. The (cid:4: (18 pts) determine whether or not the following sequences converge or diverge. Be sure to justify your answer: (cid:26) 3n+1 5 4n. Solution: (cid:27) ln 3n(cid:27: (cid:26) ln 2n, (cid:26) ( 1)n cos(n ) n (cid:27) (a) As n and the sequence diverges. Alternatively, set f (x) = ln 2x ln 3x.
