x1 x2 x3 Assuming that A is invertible, use Cramer's Rule to find the value of 2 in the solution of the equation A Let A = 4 a 1 02 b 4 c -3 x and b H 1 = b.

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A: To show that in for sufficiently large let's compute :Now, since is a smooth solution of , the…

Q: sin² x x2 goo 88 dx R TT 2

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Q: Find a root of f(x)=In(x²+1)-4 sin(x-1) with 10-3 accuracy.

A: f(x)=ln⁡(x2+1)−4sin⁡(x−1)Derivative with respect to xf′(x)=2xx2+1−4cos⁡(x−1)Now…

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Q: -1 3 -3 5 Z (0) = (1,0) dZ dt Z

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Q: 3. Suppose that p and q are odd primes. Show that pq is a pseudoprime base 2 if and only if ord,…

A: We shall be using the fact that a^p-1 =1 mod p

Q: can you write this on paper please

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Q: Follow the steps to solve the below differential equation using series methods. y'' — 5xy' – 3y = 0,…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 2. Let n₁,..., nk be pairwise relatively prime positive integers, and let n = n₁ ... nk. Recall we…

A: this is also famous known as the chinese remainder theorem

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Q: Solve Cauchy problem for the non-homogeneous equation: y" - 5y' + 4y = x-2, y(0) = -1, y'(0) = 1…

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Q: 1. Estimate the total sales during the first 6 months of the year and the last 6 months of the year.…

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Q: dx, dt = 2x₁ + x₂ +u dx₂ = -2x₁ + u dt Z = 3x₁

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Q: dx So 1+x²n 0 = π/2n sin () 2n

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: A matrix A= -10 -5 -1 40 37 -12] 20 20 -7 4 1 1 Find a basis for Nul A: 1 reduces to 0 0 -4 0 -4 3…

A: A matrix  reduces to .Find a basis for .

Q: Consider the initial value problem given below. dx dt = 3+tsin (tx), x(0) = 0 Use the improved…

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Q: 2. Let ƒ(x) = x² sin(1/x) when x ‡ 0, ƒ(0) = 0. For any a ‡ 0, find ƒ'(a).

A: Since these are multiple questions according to our guidelines we can solve only first one.please…

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Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

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Q: Consider the following function: f: Z → N given by f(x) = (x+4)² + 8; where, as usual, Z and N,…

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Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n= 4. Compare…

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Q: 2. a) Differentiate the function Q(p) = -2₁√/p³ (²-√). b) Hence or otherwise, determine Q'(1).

A: Derivative using product rules

Q: Consider Euclidean space in D = 2. Show by direct computation that the Riemann or,

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