Calendar: 1896-1897 Page 693

FACULTY OF SCIENCE cm 16 Find from first principles the differential coefficients with respect to of ax and β sin xm ix to -2T shew that χΛ 2x die Ji dx Find the 5th differential-coefficient of Λ-χ י cos r2 17 Obtain the first live terms in the expansion of sin ttfc 18 When is maximum or minimum value of given by solution of the equation j' From fixed point on the circumference of circle radius tl perpendicular AN is drawn to the tangent at Ρ prove that the maximum area of the triangle APN is י 19 Three expressions for the radius of curvature of given ds dr ר r1 fy 2Vi rf2 curve at given point are r- and ίי άφ dp dx dx State accurately the meanings of the symbols and φ and assuming any one of these expressions deduce one of the others curve is such that the centre of curvature lies on fixed circle express the radius of curvature at any point in terms of the radius of the circle and the distance of the point from the centre of the circle 20 Trace the curve determined by χ αθ 1-cos0 and determine its points of inflexion as problems YEAR If AB is any straight line and BC is drawn perpen- dicular and equal to AB CD perpendicular to AC and equal to AB and DE perpendicular to AD and equal to AB prove that AE is double of AB ABC is triangle Ε is the mid-point of AC is the mid-point of any straight line drawn from Β to AC Prove that the triangle AEG is quarter of the triangle ABC ABCDEFG is regular heptagon in circle centre Κ is the mid-point of the arc AG KB KC cut OA in and