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Trigonometry Differential Calculation
QuestionShow that f 5x2/(1 + x)1/3dx = 3(1 + x)2/3(5x2 – 6x + 9)/8 + CSummaryThe question belongs to Mathematics and it is about calculating differentiation in trigonometry.Total Word Count NA ... Read More
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Trigonometry Mathematical Induction Calculation
QuestionProve by induction or otherwise that nΣk=1 k3 = [n (n+1)/2]2SummaryThe question belongs to Mathematics and it is about calculation of mathematical induction in trigonometry.Total Word Count NA ... Read More
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Converting Trigonometric Expressions Into Algebraic Expressions
QuestionShow that the simple extension Q (cos π/9): Q is an algebraic extension and also normal extension.SummaryThe question belongs to Mathematics and it is about simple extension of trigonometric expressions into algebraic expressions.Note: The solution is in handwritten format.Total Word Coun ... Read More
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Calculation Of Rational Coefficients
QuestionThe number 1 + √2 is a root of a cubic polynomial t3 + at2 + bt + c with rational coefficients. Prove that this polynomial has three real roots and one root is a rational number.SummaryThe question belongs to Mathematics and it is about rational coefficients and calculating that the po ... Read More
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Calculation Of Galios Group Extension
QuestionProve that the order of the Galios group of the extension Q(e2iπ/17) is equal to 16.SummaryThe question belongs to Mathematics and it is about calculation of Galios group extension.Note: The solution is in handwritten format.Total Word Count NA ... Read More
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Calculation Of Extension Of Fields
QuestionLet L:K be a extension of fields s.t . [L:K] = 2. Show that if K does not have characteristic 2, then there exists θEL such that L = K(θ) and θ2EK. SummaryThe question belongs to Mathematics and it is about calculation of extension of fields. Note: The solution is in handwr ... Read More
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Conversion of Galios Group Into Algebraic Form
QuestionSuppose L: K is a Galios extension whose Galios group G is isomorphic to the Klein four group. Assume that K does not have characteristic 2. Show that there exists x, y ε k such that every element of L can be expressed in the form a + b√x + c√y + d√xy with a, b, c, ... Read More
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Calculation Of Minimal Polynomial
QuestionLet α be the real number √(5 + √21)1. Express α in the form b√x + c√y with b, c, x, y ε Q.2. Calculate the minimal polynomial of α over Q.SummaryThe question belongs to Mathematics and it is about calculation of minimal polynomial.Note: The s ... Read More
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Submartingale Convergence Theorem
QuestionLet (Xn) be a submartingale such that supn Xn < ∞ a.s. and E supn (Xn−Xn−1) + < ∞. Show that Xn converges a.s.SummaryThe question belongs to Mathematics and it is about submartingale converging.Note: The solution is in handwritten format.Total Word Count NA ... Read More
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Fixed Filtration With Respect To Martingales
QuestionFor a sequence (An) of events, show that SummaryThe question belongs to Mathematics and it is about fixed filtration with respect to martingales defined.Note: The solution is in handwritten format.Total Word Count NA ... Read More
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Calculation Of Martingale
QuestionLet (Xn) be a martingale and write ∆n = Xn − Xn−1, Suppose that bm ↑ ∞ and Σ∞m=1 b −2m E∆2m < ∞. Prove that Xn/bn → 0 a.s.SummaryThe question belongs to Mathematics and it is about martingale calculationNote: The solution is ... Read More
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Calculation Of Non-Negative Martingale
Question Let (Xn) be a martingale with supnE|Xn| < ∞. Show that there is a representation Xn = Yn – Zn where (Yn) and (Zn) are non-negative martingales such that supn EYn < ∞ and supn EZn < ∞ SummaryThe question belongs to Mathematics and it is about no ... Read More
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