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Consider the equation 1 - 2x = sin x. Use the Intermediate Value The.pdf

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Consider the equation 1 - 2x = sin x. Use the Intermediate Value Theorem to prove that this equation has a in the interval (0, pi /4). Check all the criterions in the IVT. Use a graphing calculator to find an interval of length 0.01 that contains this . Explain how to obtain this interval. Solution let f(x) = sinx + 2x -1 (it is clearly a continuous function in the given interval) now f(0) = -1 and f(/4) = 1/2 + /2 -1>0 Since f(0)< 0 < f(/4), by intermediate value theorem there exists a point x for which f(x)=0 i.e f(x) has a root..

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Consider the equation 1 - 2x = sin x. Use the Intermediate Value Theorem to prove that this equation has a in the interval (0, pi /4). Check all the criterions in the IVT. Use a graphing calculator to find an interval of length 0.01 that contains this . Explain how to obtain this interval. Solution let f(x) = sinx + 2x -1 (it is clearly a continuous function in the given interval) now f(0) = -1 and f(/4) = 1/2 + /2 -1>0 Since f(0)< 0 < f(/4), by intermediate value theorem there exists a point x for which f(x)=0 i.e f(x) has a root.

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  • 1. Consider the equation 1 - 2x = sin x. Use the Intermediate Value Theorem to prove that this equation has a in the interval (0, pi /4). Check all the criterions in the IVT. Use a graphing calculator to find an interval of length 0.01 that contains this . Explain how to obtain this interval. Solution let f(x) = sinx + 2x -1 (it is clearly a continuous function in the given interval) now f(0) = -1 and f(/4) = 1/2 + /2 -1>0 Since f(0)< 0 < f(/4), by intermediate value theorem there exists a point x for which f(x)=0 i.e f(x) has a root.