Answer the following by hand, i.e. without a computer. 1. Approximate the root of f(x) =...

 

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Answer the following by hand, i.e. without a computer. 1. Approximate the root of f(x) = x - 3, starting with the interval [1, 2], with maximum relative error & = 0.1. 2. Approximate the root of f(x) = x - 10, starting with the interval [3, 4], with maximum relative error = 0.1. 3. Apply the Bisection Method to approximating the root of f(x) = sin(x), starting with the interval [1, 99] and =0.00001. 4. Consider your result of the previous question. Can you think of a problem with applying the bisection method to this? 5. Approximate the value of the root of f(x) = -3x + 5x + 14x - 16 near x = 3 with small error. 6. Approximate the root, with sufficiently low tolerance, of f(x) = e* - 2x - 1 within interval [1, 2]. Note that e is Euler's number, equal to approximately 2.718. Answer the following by hand, i.e. without a computer. 1. Approximate the root of f(x) = x - 3, starting with the interval [1, 2], with maximum relative error & = 0.1. 2. Approximate the root of f(x) = x - 10, starting with the interval [3, 4], with maximum relative error = 0.1. 3. Apply the Bisection Method to approximating the root of f(x) = sin(x), starting with the interval [1, 99] and =0.00001. 4. Consider your result of the previous question. Can you think of a problem with applying the bisection method to this? 5. Approximate the value of the root of f(x) = -3x + 5x + 14x - 16 near x = 3 with small error. 6. Approximate the root, with sufficiently low tolerance, of f(x) = e* - 2x - 1 within interval [1, 2]. Note that e is Euler's number, equal to approximately 2.718.

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1 Approximating the root of fx x 3 We start with the interval 1 2 Lets evaluate fx at the endpoints f1 1 3 2 f2 2 3 1 Since f1 is negative and f2 is positive we can conclude that there is a root betwe... View the full answer