Find the positive real root of
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- A root of the function f(x) = x3 – 10x² +5 lies close to x = 0.7. Doing three iterations, compute this root using the Newton- Raphson method with an initial guess of x=1). Newton-Raphson iterative equation is given as: f(x;) Xi+1 = Xị - f'(xi)arrow_forwardfor 0 < x < 1 у (х) %3 Зех - 5 Use the Bisection Method to look for a root of the equation. Begin with values of x = 0.5 and = 0.6. Complete three iterations of the method by filling out the table below. Show your %3D calculations. Xc f(x,) f (x.) Iterations Xr 1 0.5 0.8arrow_forwardUse a step size of 0.1 and round your answers to five decimal places if needed. Use Euler's method to approximate the solution x10 for the IVP y' 8y, y(0) 1. The Euler approximation for x10 isarrow_forward
- Using trapezoidal rule integration with 2 equal sized sub-intervals, find the area under the curve defined by the polynomial y = 0.04x5 + 0.5x3 + 38 between limits of 4.7 and 11.0. Give your answer to a precision of at least 3 significant figures.arrow_forward4. Using the method of Least Squares, determine to 6-decimal place the necessary values of the coefficient C1 and C2 in the equation from the given data points. 1 y = C, + C2x A C 2.07 8.60 14.42 15.8 Where: ABCDEF is your student number. Example, if your student number is 484321. A = 4 B = 8 C = 4 D = 3 5. Using the same data points given in problem 4, solve for the Newton's Interpolating Polynomials.arrow_forwardEx.15: Compute the temperature distribution in a rod that is heated at both ends as depicted in the following figure. Use Gauss- Seidel method given that:- T₁+2T₁+T₁_₁ = 0 where T, represents the temperature at any nodal point. Perform your calculation correct to five decimal places, and use (T = 0) as an initial guess. To = -10 °C T₁ x T₂ T3 Ts = 10 °Carrow_forward
- 3. 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_forwardx^2-5x^(1/3)+1=0 Has a root between 2 and 2.5 use bisection method to three iterations by hand.arrow_forwardCompletely solve. Box the final answer. WRITE LEGIBLY OR TYPEWRITE THE SOLUTIONS. Prove that the steady-state solution is yp = 4.8 sin 3t - 7.6 cos 3arrow_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_forwardUse bisection to determine the drag coefficient needed so that an 80-kg parachutist has a velocity of 36 m/s after 4 s of free fall. Note: The acceleration of gravity is 9.81 m/s2 . Start with initial guesses of xl = 0.1 and xu = 0.2 and iterate until the approximate relative error falls below 2%.arrow_forwardmathforadmi..2dff1dd723 PTU Kadoorie sygini 1930 Technical Department of Applied Mathematics Second Semester 2020/2021 Math for Administration Assignment 2 Question 1 For the function: y = 0.01x- 0.001x² Find the zeros, the vertex and the optimum value (max. or min.) Question 2 Suppose a company has fixed costs of $300 and variable 3 costs of x + 1460 dollars per unit, 4 where x is the total number of units produced. Suppose further that the selling price of its product is 1500 X- ♡ lar Fine break-even points. init. II جامعة Palestine ||arrow_forward
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