Calendar: 1859-1860 Page 443

444 GENERAL LITERATURE AND SCIENCE II -HBiJTerential anS integral Calculus Find the third differential coefficient of tan-1 Vl ir2- xx If 11 be maximum or minimum when χ show that du d"1 -j- and in general -t Έχ 2ί α -a 2a -ζ 3β ϊ χ3 Expand sin according to the powers of π π χ Find the value of tan when Define tangent to curve and thence find its equation and show if and χ be the co-ordinates of the point of contact yx and of the foot of the perpendicular on the tangent from the origin that p2 xXi yyv If be the area of curve defined by rectangular co- ordinates by polar co-ordinates prove dA dA x3 Ex V2 s- from χ to χ 2r 2a ך-- from θ to θ י -י cos ί Define the circle of curvature to curve find its radius and the co-ordinates of its centre 10 Find the radius of curvature and evolute of the ellipse du2 11 In spirals if show that 12 Find the equation between and when r2 a2 cos Θ r2 sin 2a2 SP 30 13 Integrate χ2