Calendar: 1861-1862 Page 497

498 GENERAL LITERATURE AND SCIENCE Ex Find value of 313 Ix1 27 IS 13 -7 27 -18 WheD Ex And of sin χ sin ii cos χ cos χ Expand 8in -1 χ and log according to the powers of and compute four terms of the first series when χ ג יי a-x x- 2e race the curve denned by 11 χ--- Differentiate the following functions of χ bx -I י י tan log tan3 χ tan χ χ Find the equation to the witch and determine the points of contrary flexure and the radius of curvature at any point Find the equation to the tangent of curve to rectangular co-ordinates and deduce the value of the subtangent Define an asymptote and find one in case of the curve of which the equation is y3 Investigate the equation to the polar subtangent and find the locus of the extremity of the perpendicular on tangent when ן a2 cos Θ 10 If be the surface of solid of revolution and be an arc and and χ the co-ordinates of its extremity prove that χ π dx Let the generating curve be an ellipse find in terms of χ and the eccentricity