Calendar: 1858-1859 Page 422

424 GENERAL LITERATURE AND SCIENCE and apply it to the fraction when χ χ Ta x-l Evaluate ך -f -- when 22 ί2χ- Find the maxima and minima values of x3 18 2- 48 λ and of x- Find an expression for the angle which the tangent at any point of curve makes with the axis of Ex In the curve xy 6y2 at the points whose abscissa is Show how the points of inflexion in curve may be deter- mined and find those of the curve a3y3 b3 x3 a3b3 Having given the equation to spiral between and show how to find that between ρ and Ex sec η θ 10 Trace the curves y2x r-4 sin θ cos cos 11 Integrate the following differential coefficients 62 -1 iT5 י f-T67 4s24 τ2 Γ III robltms If are the three angles of triangle then tan tan Β tan tan tan Β tan Find the side of the equilateral triangle whose angular points are in three given parallel lines Find the locus of the foci of parabolas which have given directrix and which touch given straight line Determine the equation to the ellipse whose centre is at the origin and which touches the lines χ -f- 2y and χ yy Find the locus of point such that if line is drawn through it in given direction to cut given circle the ratio of the inter- cepted parts may be constant The surface of rectangular parallelopiped is 48 fr and its