4- Find the volume of the solid generated by revolving the region about y-axis,the region in the first quadrant bounded above by the parabola y=x2,below by the x- axis ,and on the right by the line x-2.

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Q: Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

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Q: 3) y" + 16y = 1, y(0) = 1, y'(0) = 2;

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Q: 8. Let X be a set and ß be a basis for a topology T on X. Then T equals the collection of all unions…

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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Q: hird-order Euler equation is one of the form ax y"" + bxʻy" + cxy' + ky = 0, where a, b, c, and k…

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Q: 3. Let (0 < x < 1) x; f(x) = { (1 < x < 2) 2x; i) Is the function f(x) continuous on [0, 2]? Explain…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: use Laplace Transform to solve the following differential equation d²y(t) + 6) + 8y(1) = u(1). (0) =…

A: differential equation:d2ytdt2+6dytdt+8yt=ut; y0=0, y'0=1We have to solve the differential equation…

Q: 3. Let D, and R, be the domain and range of f. Let D, and R, be the domain and range of g. Use the…

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Q: Question 7. Solve the following initial-boundary value problem modelling the vibration of a string…

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Q: Problem Set: Using the trapezoidal rule with n = 10, estimate the value of the definite integral.…

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Q: Evaluate the line integral F. dr, where C is given by the vector function r(t). F(x, y) = xy i + 9y2…

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Q: 14. Evaluate. dx xvx2-1

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Q: The graph with two vertices is Hamiltonian. True False

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