Calendar: 1851-1852 Page 366
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370 THE SCHOOL III -Differential Caleuto Find the differential of the length of an arc to rectangular coordinates and deduce from the result the property that the chord and arc are ultimately equal Find that cone which inscribed in sphere shall have the greatest surface Define the radius of curvature and from the definition tint the radius of curvature to spirals Apply the expression to the spiral and show that the successive distances at which the curve cuts the original distance form series of this nature זי י &C l' c4 l' c6 1' Draw tangent to any curve apply the method to rf and find the length of the perpendicular from the origin upon the tangent χ Expand ei to terms according to the powers of Draw an asymptote to y4 xy Find the differential coefficients when J"x x-1y 35a χ χ-l ----- cot cos χ sin χ ύ Find the value of the fractions 10 χ sin when χ sin χ f- λ α χ χ Jx a9 when χ
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