Consider the following equation. cos X = X^3 (a) Prove that the equation has at

Question

Consider the following equation. cos X = X^3 (a) Prove that the equation has at least one real root. f(X)= cosx- x^3 is continuous on the interval [0, 1], f(0) = 0 and f(1) = cos 1 ? 1 0.46 0. Since -0.46, there is a number c in (0, 1) such that f(c) = O by the Intermediate Value Theorem. Thus, there is a root of the equation cos X -x^3 = , or cos x = x^3, 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.)

Explanation / Answer

(0.86,0.87)

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