Let f(T) and g(T) be polynomials in Q[T] whose gcd in Q[T] is 1. Show that 1 is also their gcd in C[T].

Q: Solve for a root/roots of the functions x² – 3 sin x + 2 In(x + 1) = 3.5 Applying the following meth...

A: Newton Raphson Method:-

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Q: 1. Find all the distinct values of (1 – i)5/4, then plot the results on an Argand diagram.

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Q: Graph the linear inequality y ≥ 3x + 5

A: We have to draw graph of linear inequality  y ≥ 3x + 5 

Q: : Solve the following first order differential equations Use any method: 1. e + 2x dx + e x dy 0 %3D

A: Since you have posted a multiple question according to guildlines I will solve first question for yo...

Q: Obtain an asymptotic expansion for I(z) = S e-zy°/2 cos y? dy, along [0, 0). as z → 00 -00

A: As per the question we have to find an asymptotic expression for the integral I(z). And we will do t...

Q: HoW it aくく! -(メ)す |<X<2

A: We have given function ,  f(x) = 1 , 0 &lt; x &lt; 10 ,1 &lt; x &lt; 2 We know that Fourier series i...

Q: Consider the function f : [-1,2| → R defined by f(x) = x2 – 1. - On the interval[-1,0] the maximum v...

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Q: n² +1 (b) +1 n=1 (c) n3 5" n=1 (-1)" Vn +1 (d)

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Q: f'(2) for (x- x)(x² +2)(x² +x- 1) S(x) = %3D x + 2 O 676/5 O 379/7 O 587/3 O 384/9 O 585/4 O 699/7

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Q: 1. Show that x^2 - y^2 = (x – y)(x + y) for all x, y in a ring R if and only if R is commutative. %3...

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Q: Q5: Find the eigenvector and eigenvalue for A = [4 1 21 [2 0 1 B = 0 1 0 Lo 2 11

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Q: Find the sum of the convergent series. 1 1 (a) 2n 3n (b) (sin 1)" n=1 9. (c) 8+6+ 27 +... 8 1 ( d) Σ...

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Q: 1z 2x² + y%, (1) z = 2 y;

A: Solution:-

Q: One of your classmates makes the claim that the solution of an optimization problem modeled by a qua...

A: Given: Claim: The solution of an optimization problem modeled by a quadratic function occurs at the ...

Q: Question 1. Let G is a finite group and ø : G → G' be a surjective homomorphism (that is, o is a hom...

A: Given: A finite group G and ϕ:G→G' is a subjective homomorphism. To show: If G' has an element of or...

Q: 4(cos 190°+isin 190°) If A = B = (-1+ i)10 and C = 40e3", 2(cos 70°+isin 70°) solve for A + B + C. E...

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Q: Mrs. Gan gave ₱50,000 for the club fund of the upcoming school fair. The Math, Science and Art Club ...

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Q: The depth of water in a harbour varies as a function of time. The maximum depth is 9 feet and the mi...

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Q: B: Represent the region shown in figure (2) by double integrals of order dydx, dxdy and rdrde. y = V...

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Q: Consider the following planes. 3x + 4y - z = 28 x - 8y + 2z = 0 (a) Find the angle between the two p...

A: We need to find the angle between the given two planes and parametric equation of line of intersecti...

Q: If we take an adequate substitution, the following Bernoulli's equation y' +y = -x®y5 will be transf...

A: We have to find the transformed equation using an adequate substitution.

Q: C. Provide the steps and reasons to establish the following logical equivalence: 1) [Gv)→(pnar)]epng

A: As per our company guidelines, we can solve first question for you. If you want other question to be...

Q: "The product of two negative real numbers is positive" Is given by? Select one: O a. 3x Vy (x 0)) O...

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Q: If P1 is (3,5,00, P2 is (-1,2,7), and P3 (6,0,2). Find the shortest distance of the line P1P2 and P1...

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Q: . f(x) = 2* DA. O(x²) DB. Ω(x) Dc. O(x²) f(x) = [x][x] (floor of x times ceiling of x) DA. O(x²) DB....

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Q: Find the solution of the equationln(x + 2) – e¯* = 0. Using secant method with = 0 and x, = 0.5 Xo %...

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to approxi...

Q: In Exercises 1-4, use the comparison test to confirm the statement. In Exercises 15-21, use the rati...

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Q: A curve is drawn on a parabolic cylinder so as to cut all the generators at the same angle. Find the...

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Q: Which one of the following is the vector equation of a plane containing the points: (4,0, 3). (1, -1...

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Q: Find the values of the unknowns using any method applicable. 5а + 2b — 6с + 4d - е %3D 6 2а - b — с ...

A: Given system is  5a + 2b- 6c + 4d – e = 6 2a – b -c- d = -1 3b + 3c + d = 0 3a + 4b – 1.5c + 5d + e ...

Q: p(x)}. Find the dimensions of W1, W2 and Wı0 W2. 3. Determine the following for the matrix A. (a) Fi...

A: Note that the following is written as text at the top of your question post: "Please a and B part of...

Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos (w,t...

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Q: Suppose fis a real valued function defined on an open interval I and differentiable at every x eI. I...

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Q: The velocity (in m/s) of a rocket is given as a function of time (in seconds). The table below shows...

A: The acceleration is calculated by differentiating the velocity function with respect to time. The je...

Q: 2. S csch-x coth x dx

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Q: 2(s+1) What is L¯' s- using Completing the Square? + 2s +10 А. 2e cos 3t 4 -e sin3t 3 В. 2е сos 3t 8...

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Q: Choose the correct ordered pair that makes the inequality true.  ? + 3? ≤ 6             (4,−1), (5,...

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Q: 11. A group of researchers found that people prefer training films of moderate length; shorter films...

A: The double derivative test is used to optimize (maximize or minimize) a function. Follow the steps b...

Q: Given points P(4, -2, 5), Q ( 3, 2, 7), and R(-3, 2, 4)  makes up a triangle. Determine the magnitud...

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Q: Find F(s) for f(t) = sin? 4t

A: Solution

Q: Solve the differential equation using series: (x + 1)y'' - (2 - x)y' + y = 0.  where y(0) = 2 and y...

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Q: Two large containers A and B of the same size are filled with different fluids. The fluids in contai...

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Q: y = e-3* is a solution of the differential equation - - 6y = 0 dz2

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Q: Q1: By using Gaus -Jordan elimination method solve the following system : x+ y +z = 1 2x – 2y + 2z =...

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Q: Show that the eigenvalues of the Sturm-Liouville system dy + Ay = 0 dx? y(0) = 0, y(L) = 0 %3D gre a...

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Q: (a) Find parametric equations for the line through (S, 5, 6) that is perpendicular to the plane x-y+...

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Q: A breeder reactor converts relatively stable Uranium 238 into the isotope Plutonium 239. After 15 ye...

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Q: Use Taylor series for y(x + h), y(x – h), y(x + 2h), and y(x – 2h) to derive the FD formula for the ...

A: Here we have to use taylor series for y(x+h) , y(x-h) ,y(x+2h)  and y(x-2h)