# Calendar: 1867-1868 Page 487

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488 GENERAL LITERATURE AND SCIENCE If sin χ sin then shall 5g Find the values when χ of sin ע sin mx tan -ן- and 1- ע cos χ cosmx χ What values of χ and will make maximum when 11 xy y2 as -נ y1 Find the equation to the tangent of any curve find that of x'ty a' and the angle which the curve makes with the axis of χ at the origin Through given point Ρ line is drawn meeting the axes in and find its position when OA -j- f- is greatest Draw asymptotes to the curves 2a 41 3x x2 The curve 2ax2y axy1 a2y' has cusp at the origin 10 The curve 2f Saty2 2a2 a4 has double points find them 11 Trace the curves ί sin θ eosa 12 Find the radius of curvature to and evolute of the parabola 13 Integrate the following differential coefficients δχ χ3 2x2 2t x- 2' 14 Also sin3 θ cos" Θ Xs log 15 Prove ί -L log tan Jsinif cos 16 If volume of solid Ό 7ry2 dx Find when ry β ζ γ ά2 ι2 from χ to χ 17 Find the length of the curve defined by ay4 r5 18 cone is inscribed in segment of sphere compare their magnitudes and show if their altitudes be indefinitely diminished their contents are as

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