Calendar: 1887-1888 Page 673

GENERAL LITERATURE AND SCIENCE 677 Find the locus of the centre of circle which shall always toucli given circle and given straight line Prove that the tangent at any point of parabola meets the directrix and latus rectum produced in two points equi- distant from the focus Define the differential coefficient of function of one independent variable and give geometrical representation thereof Deduce from this definition the differential coefficients of the following functions of χ χ ax I0ga&s sin tan Find the 4th differential coefficients of cos log and xn- ogx 10 Find the coefficient of x5 in the expansion of log iT by Maclaurin's series 11 The angle between the radius vector and the tangent at point Θ being φ find expressions for tan ψ the polar subtangent and subnormal 12 cistern open at the top and having square base is to be covered with superficial feet of lead Find the dimensions of the cistern 80 that its capacity may be maximum 13 Explain the meaning of and give the notation for the definite integral of continuous function φ χ taken between the limits and What relation exists between such an integral and any function which has φ χ for its differential coefficient 14 Find the values of the integrals dx and taken between the limits χ and χ