# Calendar: 1889-1890 Page 756

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110 ENGINEERING DEPARTMENT If prove that and find the ratio of χ χ if Show how to find the differential coefficient of Ihe product of two functions Write down the differential co- efficient of tan 10 Find from first principles the differential coefficients of sin χ and of tan-1 11 If be defined as quantity such that ex dx prove that if X2 X3 Λ Βχ then Assuming that ax αχφ α prove by changing χ into dx 1x and afterwards changing into in the original equa- tion that φ α ηιφ α 12 Find the limit of tan 5x tan χ r- -- and of cos 2x when χ sin χ sin 13 ABO is triangle and PQPS an inscribed rectangle ϋ £ being in show that the cylinder formed with PS or QJR for height and P$ for circumference will have the greatest volume when PS one third of the distance of from BC 14 Find rectilinear asymptote of the curve 40 ע -4 algebra ants Cngonomctn Find th& 10th term and the sum of 20 terms of the series 24 21 18 15 how many terms of the series must be taken that the sum may be 99

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