Use the Intermediate Value Theorem to show that there is a root of the given equation...

  

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Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. e* = 4 - 3x, (0, 1) The equation e = 4 - 3x is equivalent to the equation f(x) = e* - 4 + 3x = 0. f(x) is continuous on the interval [0, 1], f(0) = and f(1) = . Since ---Select--- v <o< ---Select-- there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation e = 4 - 3x, in the interval (0, 1). Need Help? Read It Talk to a Tutor 16. + -15 points SCalcET8 2.5.057. My Notes Consider the following. cos(x) = x3 (a) Prove that the equation has at least one real root. The equation cos(x) = x3 is equivalent to the equation f(x) = cos(x) - x3 = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = Since ---Select--- <o< --Select--- there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x3, 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. Round your answers to two decimal places.) Need Help? Read It Talk to a Tutor Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. e* = 4 - 3x, (0, 1) The equation e = 4 - 3x is equivalent to the equation f(x) = e* - 4 + 3x = 0. f(x) is continuous on the interval [0, 1], f(0) = and f(1) = . Since ---Select--- v <o< ---Select-- there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation e = 4 - 3x, in the interval (0, 1). Need Help? Read It Talk to a Tutor 16. + -15 points SCalcET8 2.5.057. My Notes Consider the following. cos(x) = x3 (a) Prove that the equation has at least one real root. The equation cos(x) = x3 is equivalent to the equation f(x) = cos(x) - x3 = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = Since ---Select--- <o< --Select--- there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos(x) = x3, 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. Round your answers to two decimal places.) Need Help? Read It Talk to a Tutor

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