# Calendar: 1874-1875 Page 556

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556 GENERAL LITERATURE AND SCIENCE ax by cz a1x ctz may have common line of intersection 15 Investigate the equation to cone enveloping the ellipsoid a2 A2 c2 and having its vertex at given point If through the given point similar similarly situated and con- centric ellipsoid be drawn prove that this will meet the cone again in plane curve and that this plane will touch the ellipsoid if the vertex of the cone lie on the ellipsoid a2 Η c" VII -Btffcrenttal anil integral Calculus Differentiate the following functions xx sin-'a a2 x2 tan -- -- si η and find the value of the last when χ is indefinitely small If άφ ζ if joes 110t become infinite dx between χ and χ and if the interval is divided into intervals hvhv hn prove that φ φ is the limit of the sum of the series ---- ---- hn hn when the number of the intervals is indefinitely increased and their magnitudes are indefinitely diminished If be real function of which together with it' derivatives remains continuous between the limits and -4 and if and its derivatives as far as the χ 'd vanish when χ show that -5 00 י ίΑ if Θ denote number less than unity

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