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Determine the real root of
(a) Graphically.
(b) Using bisection to locate the root. Employ initial guesses of
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- 8. Use the Lagrange multiplier method to find the point on the line 3x + 8y = 146 that is closest to the origin.arrow_forward2. Answer the question completely and write down the given, required and formula that had been used. Provide graph and accurate/comple solution. The value are: V- 1 X- 5 W- 7 Y- 6 Z- 8arrow_forward3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0arrow_forward
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- 3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0arrow_forwardThe values of p and h which renders (makes) the following set of equations dynamically and statically decoupled are, respectively. k,+k2 5 p+4 x1 = 0, X2 7 h+1 + [7h+1 J+e 5 p+4 J+e h= -0.214 and p = -1.76 h = -0.143 and p= -0.8 h = -0.281 and p= -1.2 h = -0.081 and p = -0.536arrow_forwardGiven the data below: Xo = 1 X1= 2 x2 = 4 Axo) = 2 Ax1) = 3 Ax2 : = 8 (i) Calculate the second-order interpolating polynomial using the method of the Newton's interpolating polynomial. (ii) Use the interpolating polynomial in (i) to calculate the approximated/interpolated functional value at x = 3, i.e., (3). (iii)Calculate the percentage relative error if the true value of f(3) is 4.8.arrow_forward
- a) b) c) Use composite Simpson's rule to estimate xe*dx with n=4. Subsequently, find the absolute error. dy dx Given 3y + 2x, where y(0) = 1 and h = 0.2. Approximate the solution for the differential equation for one iteration only by using Runge Kutta method of order two. Set up the Gauss-Siedel iterative equations the following linear system: 6x₁-3x₂ = 2 -x₁ + 3x₂ + x3 =1 x₂ + 4x₂ = 3 (Do not solve)arrow_forwardFrom the following graph identify the steady-state maximum force. 1.2 1 0.8 0.6 0.4 0.2 0 Electical Power 1 Force vs. Time 2 Time (s) m 4 5arrow_forwardDetermine if the system is consistent or inconsistent. Justify your answer and find all solutions to the system of linear equations. Justification should be written on your solution paper. Transform the matrix into ROW ECHELON FORM (REF) using row operations. 2x +8y+ 6z = 20 4x+2y-2z =-2 3x-y+z = 11 Enter final answer: (x, y, z) =(arrow_forward
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