Consider the following equation. cos x= x (a) Prove that the equation has at least one real root. Pv0 7 -0.46, there is a number f(x) = cos x - x is continuous on theinterval [0, 1], (0) = c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos x - x- ?0, and f(1) - cos 1-1- -0.46 ?0. Since or cos xx, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation.)

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