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
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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.
What to read after Papers Set in the Mathematical Tripos in the University of Cambridge 1913 191?
You can find similar books in the "Read Also" column, or choose other free books by University of Cambridge to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Papers Set in the Mathematical Tripos in the University of Cambridge 1913 191?
You can find similar books in the "Read Also" column, or choose other free books by University of Cambridge to read onlineMoreLess
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