Calendar: 1869-1870 Page 514

516 GENERAL LITERATURE AND SCIENCE tan-1 ν ax tan1 JXf7it mml Vi-r-5 -j- χ log tan JL י V4 cos If sec ear By Maclaurin's Theorem show that log log ------ &c 8"2יχ2 4Τ -sin 1x 2sin2 r- sin The value of--- -is when χ cos cos and when χ 1- V2 If be the area of curve defined by or dA dA 2Sr Let the curve be the Cissoid 5ע --- 2a χ Ex The Lemniscata r2 cos 26 Given the base 10 feet of triangle and its vertical angle 60 find when its area is maximum and the lengths of the two sides 10 stone of rectangular form and feet thick contains 768 cubic inches find the length and breadth when its surface is greatest 11 QSq and PSp are two chords drawn through the focus of an ellipse at right angles to each other find when Qq Pp are tbe greatest possible 12 In tbe curve χ show that the tangent is parallel to the axis of when χ and that a2 cuts the axis of χ at 135