# Calendar: 1899-1900 Page 769

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FACULTY OF SCIENCE Solve the equations Ix my nz l2x m2y n2z M2 n2e ζ Find as determinant the product of two determinants each of three rows and columns Shew that if xx ax2 by2 y1 cx2 dy29 where ad be and x3 b'y3 y2 cfx3 d'y3 where a'd' b'c' then xx r3 42 y3 yx βτ3 Dy3 where Shew that between every two roots of there is at least one root of If more than one root of lies between then for certain values of the equation has an even number of roots in excess of those which possesses between these limits Find the equation whose roots are the squares of the differences of the roots of x3 -px Shew that if the roots γ of the cubic equation x3 px2 qx are in then q3 p3r 10 Find all the roots of 21 8x3 66a Ιδδχ 50 given that some of them are commensurable 11 Examine the nature of the roots of 7x3 -7 50-0 and find one of them to four places of decimals iii ttferenttal anb Integral Calculus Define differential coefficient and find from first principles the differential coefficient of tan sin-1 10ge Differentiate with respect to χ ax2 cos ί" Αχ2 State nd prove Leibnitz's Theorem

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