Find the root of the equation x = cos(x). In this problem, you may assume that...

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Find the root of the equation x = cos(x). In this problem, you may assume that cos(x) is continuous at all real numbers. You may also use a calculator for the computations. 1 (a) Show that the equation x = cos(x) has a solution in the interval [0, 7/2] [Hint: to use the IVT. you need to define a function f(x) and find an appropriate s such that f(x) = s corresponds to a root of x = cos(x).] (b) Use a calculator to compute f(7/4) for the function f(x) defined in part (a). Use this value, togehter with the IVT (with the same function and the same values as above) to show that there is a solution of the equation x = cos(x) in one of the two intervals [0, π/4] and [/4, 1/2]. Make sure to tell the reader which interval contains a root. (c) Let c be the midpoint of the interval at the end of part (b). Using the same logic as in part(b), explain which half-interval you can find a root in. Find the root of the equation x = cos(x). In this problem, you may assume that cos(x) is continuous at all real numbers. You may also use a calculator for the computations. 1 (a) Show that the equation x = cos(x) has a solution in the interval [0, 7/2] [Hint: to use the IVT. you need to define a function f(x) and find an appropriate s such that f(x) = s corresponds to a root of x = cos(x).] (b) Use a calculator to compute f(7/4) for the function f(x) defined in part (a). Use this value, togehter with the IVT (with the same function and the same values as above) to show that there is a solution of the equation x = cos(x) in one of the two intervals [0, π/4] and [/4, 1/2]. Make sure to tell the reader which interval contains a root. (c) Let c be the midpoint of the interval at the end of part (b). Using the same logic as in part(b), explain which half-interval you can find a root in.