# Calendar: 1874-1875 Page 558

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558 GENERAL LITERATURE AND SCIENCE Fh1d the multiple points cusos conjugate points and points of inflexion of the curve bf when is greater than equal to and less than 11 Show how tlie asymptotes of curve may be found when it is referred to rectangular polar co-ordinates Find the asymptotes of the following curves xy2 -4 ζ 3λί αό b3 ab sin30 a2eos0 12 Prove that the curve has ramphoid cusp at which the two branches have the same curvature that the tangent at the cusp meets the curve again when and that it has point of inflexion when Λ 64a4 χ A---1 τ 225 cV 13 Integrate sin1 χ cos -f- sec χ -f- χ2 V1 Shew that dx -f- iiosj b2 cosnxdx π Jo1 b2 lusx bn ai £2 14 Find the area of the loop of the curve 2a and the length of the arc measured from the vertex to any point Prove that this length is equal to the intercept of the normal on the axis of and that the radius ot curvature at any point normal 2a

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