Papers Set in the Mathematical Tripos in the University of Cambridge 1913 191
Papers Set in the Mathematical Tripos in the University of Cambridge 1913 191
University of Cambridge
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1915] MATHEMATICAL TRIPOS. PART I 41 8. State Taylor s theorem, and apply it to express sin (TT + 6) in a series of powers of 6. Find by Maclaurin s theorem the expansion of as far as the term in a? ; and shew that no even powers of w can occur in the expansion to any number, of terms. 9. Why is 3J regarded as the measure of the curvature at a point of a plane curve, in which s is the length of the arc, and if/ the inclination of the tangent to a fixed line 1 Prove that in rectangular Cartesian... coordinates ds dx 2 \ \F> and shew that at any point (x, y) of the curve the measure of curvature is \ ab (ax + by) ~. 10. Solve the differential equations (i) sin x -/- - 2y = tan 4 - ; dx (ii) -j- + ri*x = k smptj considering in (ii) the cases when p and n are unequal and when they are equal. FRIDAY, 4 June. 9 12. 1. A string OABCD is attached to a fixed point 0. A weight W is hung from each of the points A, B, C, and the position of D is such that CD is horizontal and the tension in it is W.
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