# Calendar: 1879-1880 Page 597

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GENERAL LITERATURE AND SCIENCE 597 13 Construct the following conies xy ay ax a2 cot β ay c5 finding the latus rectum of the former and the transverse axis of the latter 14 straight line moves parallel to the plane and intersects the curves z2 mx ζ ya mx prove that the locus of its trace on the plane of yz is two straight lines at right angles to each other 15 Find the cosine of the angle between the two straight lines represented by Ix my nz and axi fy cz XVII -JBifferenttal anb SnUgral Caltului Differentiate ן as sinx tan χ If cos sin Jir prove that 1- -4 ל aur ax Enunciate and prove Leibnitz's Theorem Find the th differential coefficient of COSiT Evaluate xx χ-x ogx when χ Show how to find the maximum and minimum values of function of one independent variable Given the centre of an ellipse and fixed point upon it and the direction of the principal axes determine the ellipse when the diameter conjugate to that through the fixed point is minimum

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