Calendar: 1871-1872 Page 521

general literature and science 521 Expand in ascending powers of if log cos ע xsmy Find the limiting value when χ approaches zero of tan- 1x tan SJH£ sin מ cos sin π sin If χ tan -1 show that when χ -1 -12 If cos χ sin 2ל then Show how to find the maximum and minimum values of function of one independent variable circle is described about segment of parabola cut off by double ordinate perpendicular to its axis show that the length of the greatest chord of the circle which is tangent to the parabola is equal to the abscissa of the segment If ζ χ φ ψ prove that ο d2z d2z ad2ζ dx2 dy 0- 10 Find the nature of the point at the origin in the curve a3y2 abx2y -Xs and the rectilineal asymptotes of x2y axy2 ax3 c2y2 11 If and ρ are the radius vector and perpendicular from the pole on the tangent to plane curve and p' the perpen- dicular from the pole on the tangent of the curve which is the locus of the point of intersection of the perpendicular on the tangent with the tangent prove that p2 rp1 Find the polar equation to the normal at any point of curve