8. Use the method of Laplace transform to solve the initial value problem y" – 20y + a?y = (a – B)²et, y'(0) = y(0) = 1+ a, = aa + B + b.|

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: (b) у" — 4у'+ Зу %3D Зе2х + 4е* + 2e3х

A: Given differential equation: y''-4y'+3y=3e2x+4ex+2e3xTo find: General solution of the differential…

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A: We will find point of intersection. Derive slope of tangent for.polar curve and then substitute…

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A: Given series is ∑n=2∞(x+101)n2ln(n)

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

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Q: Determine all minors and cofactors of -3 -3 -9 A = |-4 7 -9 9 -2 9 М— C =

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Q: ... Find the general solution of the system of linear differential equations (expr83s your answer in…

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Q: romises are sincere.

A: Option a - some  campaign promises are sincere

Q: Question 7. Using induction prove that 13 + 23 +... + n³ = + u)u for n > 1.

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Q: he curve y = X fc (vî (yi

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Q: 3. Which of the following is always true for any real nur O For real ɛ > 0, if x-yl s &, then x = y…

A: 3. For 1st option: let  x = y + ∈ then |x-y| ≤ ∈ but  x ≠ y So option 1 is incorrect. For 2nd…

Q: If vi = (1 2 2], v2 (0 0 1), v3 (1 2 3] then (vi + V2, v2 + V3) is b) 15; © 17; d) 11; e) 3; f)

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Q: The following table shows the results of a

A: Given, the following table shows the results of a survey of 400 authors by a publishing company.…

Q: z) = (x2 + then (a + E

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Q: 1. The area B is given by = {(r, y, -) € R* | + <1,: =-, y? { (x, y, z) E R² | 1, 2 = r² – y² В…

A: Given that B=x,y,z∈ℝ3 | x24+y29≤1, z=x2-y2 and the vector field assign for Stokes's integral theorem…

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A: Solution :      Let us define the following symbols: mr : I was replacing my calculator batteries in…

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Q: 4. Find all real values of x such that |x-1| > |x+1]. * (-00,-1] (-00,0) [-1,0) [-1,1) None of the…

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Q: Example 6.9. One entry in the following table is incorrect and y is a cubic polynomial in x. Use the…

A: y is a cubic polynomial in x. We can use difference table to solve

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A: Since you have posted a multi subparts question according to guildlines I will solve first three…

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A: We have to show that there is a statement which is equivalent to Archimedian property.

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Q: Find the area of the region bounded by the curvesr = 2 cos 30 and x = y – 1.

A: The curves given are as follows: r=2cos3θx=y2-1 We know that x=rcos3θ, y=rsin3θ.…

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A: Given series is ∑n=2∞(x+34)n2ln(n)

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Q: The logistic function ranges from 0 to 1 and has an 'S' like shape to it. O True O False

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Q: 4965 4 mod 5 4965 = 2 mod 7 4965 = 1 mod 11 Use your answers above to find the canonical…

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Q: Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

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Q: pes the series E (- 1)n+ 1_^_ n+2 converge absolutely, converge conditionally, or diverge? n-1 hoose…

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Q: Example 3.37. Solve the equations 2x2 + 3xy + y? = 3, 4x² + 2xy +y = 30 correct to three decimal…

A: Here, We need to use the newton-raphson method. x0 = -3 y0 = 2

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A: To find the solution of the equation fx=0, apply the Newton's method formula xn+1=xn-fxnf'xn Where…

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Q: Discrete Fourier Transform (DFT) of x[n]=(0.9)" for 0<n<3. → X pET[k] = {2,3j,4,–3 j}using the…

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Q: The trial solution for the non-homogeneous equation d'y + 9y = 1+ xe* is dx²

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Q: Solve for the indicated higher-order partial derivatives, fræ, fxy, fyy. • f(x, y) = Vx2 + y?

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A: To determine the series converges or diverges.

Q: Answer  1)  4-1 2) 2 Intersection 4  3) (2 U 3) - 1

A: The following graphs are determined as shown below.