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  Item Reference: KCLCAL-1888-1889-748

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740 engineering department algebra differential Calculi &c Explain what is meant by determinant and evaluate the determinant be ac ab Eliminate ζ from ax by cz Prove that the convergents to continued fraction are alternately too small and too great and each nearer to the true value than the preceding If χ prove that χ Shew how to ascertain whether proposed series is con- vergent or divergent and apply your test to the series X3 xb ο χ Prove that at maximum value of where is rational integral algebraical function of dx Does it follow that whenever dy dx is maximum or minimum Find the area of the greatest rectangle that has two of its corners ony 4ax and two on χ 4a Explain the connexion of dx2 with the curvature of and prove that the curve is convex or concave to the axis of χ according as is positive or negative ax2 Prove that the evolute of the ellipse is everywhere convex to both axes
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