List of top Engineering Mathematics Questions on Numerical Methods

Given the following data: x: (-2, 1, 2), y: (28, 4, 16). Let \(P_2(x)\) be the quadratic interpolating polynomial passing through the above three points. Find the value of \(P_2(0)\).

Consider the function \(f(x) = e^{-x} - x\). Using the Newton-Raphson method, obtain the first improved approximation starting from the initial guess \(x_0 = 0.5\). Enter the value of the second approximation, correct to two decimal places.}