Calendar: 1852-1853 Page 379

THE SCHOOL 375 II -Dtffcrcnttal Calcutta Prove priori that the expansion of sin -1 cannot contain the even powers of Find the equation to the tangent to any curve and apply it to the ellipse If the tangent be drawn to point which is the extremity of the latus rectum and any point Ρ be taken in the ellipse and an ordinate Ν Ρ be drawn meeting the tangent in SP NQ ax If ν -j maximum find χ Differentiate the functions χ sin χ gV7 3- £ff a2 4abx 3b2x2 du2 Prove the equation μ spirals and apply it to the ellipse when ρ is drawn from the centre MA area of curve -- χ Trace the curve y3 x3 4- a3 draw its asymptote and shew that it has two points of contrary flexure Find the value of log when χ Δ Χ 10 Given the difference of the angles at the base and the radius of the inscribed circle find when the perimeter of triangle is maximum 11 If log a2 be the equation to curve prove that the tangent sub-tangent ordinate abscissa 12 right angle Β CP is so moved that Β and Care alwa on two axes at right angles to each other determine the locus of