Calendar: 1858-1859 Page 417

GENERAL LITERATURE AND SCIENCE 419 y2- 0-1 Or- φ y2 r2-2 when χ and when χ Find the value of when 4jr Vff Iff be function of two independent variables inves- tigate the conditions which those values of χ and must satisfy which render it maximum or minimum Find the greatest paraboloid of revolution which has common plane section with sphere and is included within it If ζ be function of two independent variables χ and and χ and be connected with two other new variables and θ by d2 ζ means of the equations χ cos sin Θ express d2z זד-ך -ך-ד in terms of the differential coefficients of ζ with dxdy dyl respect to and Θ Trace the curve x2 χ find the angle at which it cuts its rectilineal asymptote and show that it has three points of inflexion lying in straight line If be the equation to system of curves show how to find the points of ultimate intersection of two consecutive curves and the locus of these points Ex Find the envelop of the series of parabolas given by the equation Trace the curve r2 cos θ β2 cos Integrate the functions 1- י sin cos -2 χ α bx cx ""י χ ί 3χ2 χ and bx" sin β and find the area of loop of the curve r' a2 cu3 Λ Obtain formula for the reduction of Ex Integrate 5vfe