Consider the function f(x) = x - cos x, where x is measured in radians. (a)...

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Consider the function f(x) = x - cos x, where x is measured in radians. (a) Show that the equation f(x) = 0 has a root a in the interval [0, 1]. (b) Starting with the interval [0, 0.8], use interval bisection twice to find an interval of width 0.2 which contains a. (c) Taking 0.6 as a first approximation to a, apply the Newton-Raphson process once to f(x) to obtain a second approximation to a to 3 decimal places. (d) Use linear interpolation once on the interval [0, 0.8] to find an approximation to a. Give your answer to 3 decimal places. (e) Starting with a₁ = 0.4, use the iteration In+1 = COS In to calculate the values of x2, 3 and 4, giving your answers to 3 decimal places. Consider the function f(x) = x - cos x, where x is measured in radians. (a) Show that the equation f(x) = 0 has a root a in the interval [0, 1]. (b) Starting with the interval [0, 0.8], use interval bisection twice to find an interval of width 0.2 which contains a. (c) Taking 0.6 as a first approximation to a, apply the Newton-Raphson process once to f(x) to obtain a second approximation to a to 3 decimal places. (d) Use linear interpolation once on the interval [0, 0.8] to find an approximation to a. Give your answer to 3 decimal places. (e) Starting with a₁ = 0.4, use the iteration In+1 = COS In to calculate the values of x2, 3 and 4, giving your answers to 3 decimal places.

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