Calendar: 1893-1894 Page 838

cxvi FACULTY OF SCIENCE Stfftrcnttat Calatlns anil Mollis eometrp YEAR III 15 From the definition of differential coefficient find that of sj az and of sin 2x with respect to 16 Shew how the differential coefficient with respect to χ of tan-1 χ is derived from that of tan Differentiate tan-1 Sx r2 and express the result in its simplest form 17 Prove that fix hf hlf If prove that θ 18 Shew how to find the maximum and minimum values of function of two variables connected by one relation rectangle is to be cut out of circle so that the product of the th power of the length by the power of the breadth may be maximum prove that the length is to the breadth as Jn hJm 19 Find the equation of the tangent to x3 yz Sax2 at the point where χ -f meets it 20 Prove that the directions of the asymptotes of curve represented by rational integral algebraic equation in χ and depend only on the terms of highest degree in the two letters 1Λ if Trace the curve x2y2 x2 16 x2 21 Find the equation of plane in terms of its intercepts on the axes If DEF be triangle similar and similarly placed to the triangle ABC its corresponding sides being in the same order of rotation in parallel plane If the planes EFA FOB DEC meet in point prove that the perpendiculars from Η on the planes of the two triangles are in the ratio of 2μ where μ is the ratio of the sides of the two triangles 22 Write down the general equation of sphere The corners of tetrahedron are at the points Prove that single sphere