Chapter-1: Interpolation 1. Prove with the usual notations that: (a) EV = VE = A (b) A + V = (c) A= SE 2. Apply the suitable formula for the set of values given by the following table to estimate the...

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Extracted text: Chapter-1: Interpolation 1. Prove with the usual notations that: (a) EV = VE = A (b) A + V = (c) A= SE 2. Apply the suitable formula for the set of values given by the following table to estimate the value of y = f(x) at x = 0.4 and x = 3.5 0 1 2 3 4 y = f(x) -1 0 13 50 123 3. Find the interpolating polynomial for the following, using Lagrange's Method. x 0 1 2 5 f(x) 2 3 12 147 4. Develop the Divided Difference Table from the data given below and obtain the interpolating polynomial f(x) -4 -1 0 2 5 f(x) 1245 33 5 9 1335 Chapter-2: Numerical Integration and Differentiation 5. Approximate the integral x cos(x) dx using (a) Trapezoidal rule with n = 5 (b) Simpson's 3/8 rule with n 5 6. Evaluate the integral (e* + sin x+ log, x) dx by using Simpson's one third rule with n = 6.