Question 4 If + 3x + 6a2 + 12x°+... %3D then C equals 11 8. 19 8 -2 19 11 215 2/5

Q: 4) LetXbe any set with the discrete topology. Let Y be any subset of X. Prove that ô( Y ) =Ø.

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Q: 1. Use mathematical induction to prove а) 1 - 1! + 2- 2! + ... + n:n! 3D (п +1)! — 1 for all n 2 1.

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Q: If a 4 x 4 matrix A with rows ij, vz, vg, and ö, has determinant det A = 4, then det 9v1 + 9v4

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Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all z in [ – 8, 4], and / f(x)dx = 76 and…

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Q: Using a method of reduction to separable equation and reduction to linear equation, find the general…

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Q: Question Use Newton's method to approximate the x-coordinate of the point where the graph of 4x- 10x…

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Q: what is the independence number ? And give examples

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Q: Question 29 Using laws of logarithms, express 1 x2 In x + 2 x + 1 in the form A In x + Bln(x+ 1) + C…

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Q: 1. Find the general solution of the system: -6 2 X = -3

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Q: pute the Fourier sine series expansion of f(x) = 3x – x² on [0, 3]. nat value does this series…

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Q: - 1 - 1 dx ?

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Q: Find the general solution of the differential equation with clear steps.

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Q: dy Solve the differential equation: (1+ x) + y = 1+x dx with initial condition y(0)= 1

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Q: u, = and u, = Find (T]B- Verify that Formula (8) holds for every vector x in R2.

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Q: Given the definite integral | f(x)dx a you can split this into two integrals 9. S. | f(x)dx + /…

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Q: -6an-1 for n > 2 with the initial condition a = -9. an an

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Q: a. Use long division to divide 4x3+9x-12 by 2x-1 b. Write your answer in quotient form.

A: We have to perform the long division