A feedback control system modelled by the differential equation * + ax + kx = 0 is known to be asymptotically stable, for k > 0, a > 0. Set up the state-space form of the equation and show that V(x₁, x₂) = kx² + (x₂ + ax₁)², x₁ = x, x₂ = x is a suitable Lyapunov function for verifying this.

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Q: The equation y = C₁e(-x) cos3x + C₂e(-x)sin3x is the general solution of:

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (-) < 0, ƒ (x) has a root in [0, 1]. To…

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Q: Consider the function f(x) = cos x - 3x + 1. Since f(0)f < 0, f(x) has a root in [0,. To solve f(x)…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

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Q: 3s3+3s ენ

A: Here the aim is to find the inverse Laplace transform of                 L-1{3s3+3ss6}    using the…

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A: This question from numerical analysis's topic relative error.

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

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A: Here we need to find dominant eigenvalues and eigenvectors using power method.

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A: see my solution below

Q: Q5. Use Lagrange Multiplier to find the minimum distance between the origin and the line (x=51 +3, y…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (₹) < 0. f(x) has a root in [0, 1]. To…

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Q: 5. If Evaluate the following. (a) F'(9) (b) F (0), by interpreting F (0) as an area F(x) = √25 - 1²…

A: We have to find F'(9) and F(0).

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ < 0, f(x) has a root in [0]. If we use…

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Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

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Q: -2 Evaluate: £²³₁² [(x²-x²)²] du dt x+y

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Q: Problem 3. Let VCR³ be the region bounded by the planes z = 0, x= 1, and the surface defined by 2² =…

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Q: Determine whether the statement is true or false.   b) The set of all ordered triples (x, y, z) of…

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Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

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Q: Suppose 3.141516 is estimated using 3.141529. The absolute error is (Answer must be in 6 decimal…

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Q: II. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = -3 2 3 9 3 2 6 8 ㅋ

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Q: The fixed-points of f(x) = (x² + 2) are and

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Q: = 1 (x+8)2¹. y = 4 and the x-axis using vertical strip.

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Q: 3. Using Gaussian/Gauss-Jordan method solve for the unknowns: - y + 2z - w = −1 2x + y2z - 2w = -2…

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Q: Evaluate: ff xy² dx dy

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Q: Find the volume of the solid obtained when the region under the curve y = 11 arcsin(x), x ≥ 0, is…

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Q: Find the area of the region bounded by the curves y = 1 (x+4)²² y = 4 and the x-axis using vertical…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: 1. Solve the Laplace's equation 02и Ә2и + 0 Əx² дуг defined on the square 0 < x < 1 and 0 ≤ y ≤ 1…

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Q: f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

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Q: I.* Determine all the isolated singularities of each of the following functions and compute the…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)f() < 0, f(x) has a root in [0]. To solve…

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Q: 1. Suppose that (X, dx) and (Y, dy) are metric spaces and f: X →Y is a function. For a, b e X,…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ(x) has a root in [o,]. If we…

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Q: 5. If Evaluate the following. (a) F' (9) (b) F (0), by interpreting F (0) as an area F(x) = √ √ 25 -…

A: Given: Fx=∫x525-t2dt

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Q: 3 Evaluate: ³₂²₁²[z³(x + y)³] dz dy dx

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