From the table find f(1) using interpolating of Lagrange polynomial -102 Y=f(x) 2 -1 5 1 O -1 O о о 20 -20

Q: : Find the Laplace transform F(s) = {f(t)} of the function f(t) = (8-t) [U(t-4) - U(t-8)].

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Q: Let f(x) (x² + 1) cosh x² 1. It's true that Of is an infinitesimal, non-comparable with 1 ○ 13 24x4…

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Q: Question 3 Give the form of a particular solution of y"" + 2y" +9y' +18y = 3e-4 + sin(3x) - 3x.…

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Q: 3.x = 7 (mod12) x = 7 (mod15) x = 7 (mod18)

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Q: Answer only five questions. (for each question 8 Q1: Use Tayler series method to solve the initial…

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Q: rections: Complete each l polynomial expressions should be written in (5) e called the (7) alled (8)…

A: To complete the given statements on polynomials.

Q: f(t) = cos(nt) u (t-2)

A: As per the question we are given a function f(t) and we have to find the graph of its Laplace…

Q: (10) Define the metric d on R² by d( (x₁, y₁), (x2, y2)) = max{ |x₁ − x2\,|y₁ - y2|}. Verify that…

A: The given problem is to verify that the given metric d on R2. Given metric…

Q: Find the area of the region that lies outside the cardioid r = 1 - sin(0) and inside circle (r=3)…

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Q: A- The result of the following limit is 2x² + 3x lim x→∞0x³ + x + 1

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Q: Let y'= -ty + 0.1y³ and y(0) = 1.8. Use Euler's method to find approximate values of the solution of…

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Q: SOLVE X²y" + xy² - (4x² + 1 ) y = =0 BY BESSELS METHOD.

A: As per the question we are given a second order linear homogeneous differential equation and we have…

Q: Q3// Use Newton-Raphson Method to solve ƒ = -x²+x+0.75 for 5 iteration (choose 4-decimal places).…

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Q: Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0

A: Given curves are x2=8y and 2x−y=0. We have to find the ordinate of the centroid of the area bounded…

Q: Solve for the Maclaurin series expansion of ex and use the series to evaluate e0.77. What is the of…

A: Sol

Q: Using the Secant Method, for the given initial interval of [0, 2] solve for the root of the given…

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Q: The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find…

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Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: Consider the following linear transformation and basis. T: R² R2, T(x, y) = (5x - 2y, x), B' = {(-2,…

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Q: Find the radius of curvature in polar form. Derive the relation.

A: To Derive: The radius of curvature in polar form.

Q: Ecx) = sinh x X X è -èx e +---)-(1-X + X ²121 - X²/31 - + (1 + x + X/21 + X/31 2 2x+2 +2+ 3 5 2…

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Q: 1.1) SOLVE xy ¹ + 2y + xy = 0 by FROBENIUS METHOD

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Q: Q/ The management of a company for maintenance services in Khamis wants four workers to work on and…

A: The given table is    A B C D 1 5 7 9 6 2 14 13 10 4 3 15 11 12 5 4 10 17 9 11 To…

Q: Suppose that X is the space of all (bounded or unbounded) sequences of complex unmbers and dixXx X →…

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Q: Transfer the point P (6.32, 108.43°, 3) into spherical coordinate a) (5, 65.62°, 106.43°) b) (6,…

A: Cylindrical Coordinate representation: (r, θ, z) Spherical Coordinate representation : (ρ, φ, θ)…

Q: of k colourings of the cycle

A: We can do this directly using the principle of inclusion-exclusion. Labelthe vertices of Cn…

Q: 8. A spring has a natural length of 10 cm. It takes 2J to stretch the spring to 15 cm. How much work…

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Q: Problem 13. Find all solutions of the equation 2 cos x - 2 sin x cos x = 0 on the interval [0, 2π).…

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Q: 8 -8 -2 -3 3-4 Find eigenvalues of matrix A = 4 matches first eigenvalue -2, and then find…

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Q: Solve the heat transfer equation for a metal rod in one dimension, assuming a constant cross-section…

A: Method of Separation of variables

Q: Which of the following sets are closed under addition? (i) The set of all vectors in R² of the form…

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Q: Draw a direction field and plot (or sketch) several solutions of the differential equation y' = -y(6…

A: Given differential equation is y'=-y(6-ty) Direction field of given equation is

Q: (-) التاريخ الموضوع 1 1 if f(x, y) = x² cot (~) Then it is hom mogeneous Function of agree?

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Q: v=6+1-v. v(0)=1 (a) Find approximate values of the solution of the given initial value problem at t…

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Q: Q3: Solve the initial value problem by using Predictor method for two iterations: ý=y-x² +1, 0≤x≤2,…

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Q: Solve to find general solution: xef_1 1-x²y Екосев dx

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Q: Q1:Convert the Cartesian equation x²+(-a)- a to polar equation (20 marks) Q2: Check the symmetry and…

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Q: a minimal realization of H(s). For any feedback gain realization for the corresponding Hƒ(s).

A: Given, (A, B) be a minimal realization of H(s).To prove: (A-BK, B) is a minimal realization for the…

Q: Give the Laplace transform of f(x) = {₂-2, 3 ≤ x I x², 0<x<3

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Q: B- for the function below, the domain and the range is respectively −2+√1-x

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Q: 15. A flow rate of 32 microdrops per minute on a gravity system is equivalent to how many…

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Q: Solve the given differential equation. 11x² - 1 y' = 11 + 3y =

A: To solve the given differential equation .

Q: A- for the function below, the domain and the range is respectively y = |x|- 2

A: The solution is given as

Q: Find all local maxima, local minima, and saddle points for f(x₁,x₂)=x²-3xx²+x₂² (a) (0,0) iù a…

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Q: (a) Let f, g, h be continuous on the interval [a, b]. If f(a) g(b) > h(b), then there exists c =…

A: Only part (a) has been answered due to company policy, please submit other parts as separate…

Q: part

A: Here part C and D are both same.

Q: Evaluate the element a31 in the matrix A given by: a11 012 a13 A = a21 a22 a23 031 032 a33 where: A…

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Q: Draw two cards without replacement from an ordinary deck. What is the probability of the event that…

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Q: Consider the function f : I exists is continuous and str

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Q: Recall that the general solution of the 1-dimensional wave equation with fixed ends, that is, the…

A: As per the question we are given the general solution to the wave equation in form of an infinite…