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Mathematics, 29.05.2020 03:57 deasiamonay14
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. The equation ex = 6 − 5x is equivalent to the equation f(x) = ex − 6 + 5x = 0. f(x) is continuous on the interval [0, 1], f(0) = , and f(1) = . Since f(0) < 0 < f(1), 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 ex = 6 − 5x, in the interval (0, 1).
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