MH1810: Math 1

  1. A rain gutter is to be constructed from a metal sheet of width 30 cm
    by bending one-third of the sheet on each side through an angle θ: How
    should θ be chosen so that the gutter will carry a maximum amount of
    water? Express the answer in terms of π:
  2. (a) Find the derivative of the function
    Math
    (b) Find the limit
    Math
  3. (a)Math where the numbers a, b are to
    be determine.
    (b) A wedge is cut out of a circular cylinder of radius 3 by two planes.
    One plane is perpendicular to the axis of the cylinder. The other
    plane intersects the first plane at an angle of 60° along the diameter of
    the cylinder. Find the exact volume of the wedge.