Find the dimension of the splitting field of each of polynomials x+1 and x² - 2.

Q: Given the differential equation: dy y +1= dx x with initial conditions y = 1 at x = 2.0, produce a…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: e² = 4 cos(x) in [-1,1]

A: Newton's method uses the formula: xn+1=xn-f(xn)f'(xn) to approximate the root of the equation:…

Q: use Newton’s Method to find the root of the given equation, accurate to six decimal places, that…

A: The equation in the form f(x)=0 is called a transcendental equation. The solution of the equation is…

Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π

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Q: 1. Solve for the following quantities given the matrices below. 3 -5 1 L= 0.5 1 3.5 2 0 4 -j3 -3² E=…

A: Solution: Given matrics L=3-510.513.5204E=-j3-32j3ln-j35+j3j123sinj0.2-j0.5jX=133j-72-j5.5-14jj-1159

Q: Find the 103rd derivative of cos(2x).   Hint: find the first few derivatives and observe a…

A: First find nth derivative then put n=103 to find the 103rd derivative as in next step.

Q: d) must be done using Vector Calculus and the Lagrange multiplier. Optimize: the function f(x, y) =…

A: Given: The function fx,y=49-x2-y2 subject to the constraint x+3y=10. To optimize the function we'll…

Q: II. Solve the following problems. Enclose final answer. 7.Find 2 of z = 2x³-5xy² xy

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Q: 【D³ + 3D² + 3D + 2)y = 0

A: Solution:

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: (1) given,z=4-x2-y2  ( paraboloid )     _______(I)and plane: z =-1       ________(II)Put (II) in (I)…

Q: 16 Tandem Cycling Triplets Peter, Reeta and Nikita have two ways for getting home from school each…

A: since you have asked a question with multiple sub parts, we will solve the first three subparts for…

Q: Trapezoidal (Use n = 9) 5. 6. √² (5√x - ³) dx 3) (5ex-e)dx

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Q: NUMERICAL DIFFERENTIATION: Find the first derivative (i.e., general solution) then solve for the…

A: Introduction: Numerical differentiation techniques in numerical analysis estimate the derivative of…

Q: theormo- Let (Fot..) is a field and f(x) EF(x) then the ideal is maximals ideal iff fex) is an…

A: Let F be a field. Here , f(x) ∈ Fx. Here , First we assume that , f(x) is maximal ideal in Fx. We…

Q: The volume of the solid bounded by z = 0, x+y+z= 4 and x² + y² = 4 in cylindrical coordinates is 16.…

A: Solution:  True

Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

A: Solution

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: Find the Fourier transform of the given waveform. f(t) -2 -1 1 0 1 2 (s)

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Q: Using Convolution theorem find the Laplace transform of f(t) = f* r²e="dr

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Q: f(x, y) = x² − 4x³ + 2y² + 8xy+1 -

A: According to the guidelines I am answering first question only.

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: f( x) = sinx - x3 + 1 By Midpoint method f'(a) = (f(a+h) - f(a-h)) /2h

Q: For the function f(x, y) = −xy2, find the solution from x = 0 to x = 1 with an increment of 0.2 by…

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Q: 6. Find the Laplace transform of f(t) = t²e²t

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Q: Prove that the sequence {f(1/n)} has a limit if |f'(x)| < 1 for all r € (0, 1]. I

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Q: prove this: The minimal sigma field contain C is unique

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Q: x) = ln(3x 4) - cos x; f'(5)

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Q: Show all the necessary figures and solutions to each of the following problems. 2. Find the area…

A: To solve area bounded by the curve use double integral Draw the curve on x y-plane  and shade the…

Q: Q/६ using integrat test: n - 14 (n+1)(n-4) Test the following series

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Q: 5 2 d. L−¹³+; 3s-5 5s-4 e. L- L-¹1- 2s²-3¹ 1 f. L-11 s2-8s+25' 7s

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Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

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Q: Given the following: xex cos x = 0

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Q: Consider the following initial value problem y(1) = 1 y'(t) ye2t; t € [1,6]

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: A metal sphere cools from 80°C to 70°C in 5 minutes. How much more time (in minutes) will it take to…

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Q: find the graph G such that : 1) K(G) = K'(G) < 8(G). 2) K'(G) = 8(G). 3) 4) K(G) = K'(G) K(G) <K'(G)…

A: k(G) is vertex connectivity of graph G k'(G) is edge connectivity of graph G δ(G) is minimum degree…

Q: For the function f(x, y) = 4x³ + x² − 7, find the solution of the differential equation from x = 0…

A: To solve: The initial value problem dydx=4x3+53x2-7, y(0)=3, Analytically.

Q: What should be the base number “N” to make the equation 5N/44N = (0.121212…)N true? A. 17 B. 15 C.…

A: The decimal number system uses 10 as the base. In the decimal number system, the place value of each…

Q: Exercise 15.2.8 Y 1₁² Find ► Hint dA where D = {(x, y) : x ≥ 0, y ≥ 0, x² + y² ≤ 1}.

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Q: la² + 2a 2a + 1 1 2a +1 a+2 1 31 3= (a- 1)³ 1

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Q: 21. The differential modelling of the effect of a shock. absorber is given by: d'y…

A: Here the given differential equation is…

Q: For the function f(x, y) = -xy2, find the solution from x = 0 to x = 1 with an increment of 0.2 by…

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Q: a) Prove that an operator P is the pr osed linear subspace M of a Hilbert

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: The volume of a solid S in polar coordinates bounded by the surfaces z1=f1x,y and z2=f2x,y can be…

Q: 7. Find the Inverse Laplace Transform of 1 s²-8s+25

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Q: Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found…

A: Solution : Let A be quantity of radium present at time t. Decomposition equation, dAdt∝A dAdt=-kA…

Q: SHOW COMPLETE SOLUTION (NO SHORTCUTS PLEASE) (Differential Equations) The general solution of y" - y…

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Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A: This is a question of the application of calculus.

Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: Solve the following game for optimal strategy based on dominance property and algebraic method: B₁1…

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Q: [2 1. If A = 4 4 L5 1 31 1 4 3, find A-1 3 21

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