Calendar: 1863-1864 Page 525

GENERAL LITERATURE AND SCIENCE 525 13 Two points move in straight lines with uniform velocities find the equation to the surface generated by the straight line which joins them 14 Draw tangent plane to the solid defined by xyz a3 and find the content of the pyramid between it and the co- ordinate planes 15 Integrate dx from χ to χ show that יי dt between the limits of and cc 16 The volume generated by the revolution of cycloid round its axis a3 π2 16 MIDDLE MATHEMATICAL SCHOLARSHIP -Utfftrenttal Calculus CBIcmcntarg If cot-1 show that cot -1 sin Br sin 48 'u sin Sec Expand -f2 χ2 -i by Maclaurin's Theorem according to the powers of Find when dx sin-if si -y fe If sin-1 sin-1 Λ show that di 'c2 y2 "י Prove Leibnitz's Theorem for the differentiation of the pro- duct of two functions If χ show that ג ן -η2 י- χ 212 נ ג &c-