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{"ops":[{"insert":"1.Consider the equation xe^x = cos x\n\n(a) Apply the intermediate value theorem to show that the function has a root in the interval\n\n[0, 1].\n\n(b) Find the real root using the secant method. Start with the two points, x1 = 0 and x2 = 1\n\nand carry out the first four iterations.\n\n(c) Find the real root using the Newton-Raphson method. Start with an initial approximation,\n\nx0 = 0.5 correct to two decimal places.\n\n\n2.Consider the initial value problem \n\ndy = t(y + t) \u2212 2, y(0) = 2. It is derivative of y respect to t\n\n dt \n\n(a) Use Eulers method with step sizes h = 0.3, h = 0.2 and h = 0.15, compute the approximations to y(0.6). \n\n(b) Use the fourth order Runge-Kutta method Compute y(0.4) with h = 0.2.\n\n\n"}]}
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