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Unformatted text preview: Homework #3 1. Suppose f is continuous and we know that f ( x ) < 0 in [ 1 , 2] and f ( x ) > 0 in [2 . 5 , 4], find 3 approximations to the root of f ( x ) using the bisection method with starting interval [ 1 , 4]. 2. (a) Starting with the initial guesses of 1 and 2, find three additional approximations to the root of f ( x ) = x 2 2 using regula falsi. (b) What is the bound on the absolute error of the final approximation? What is the actual absolute error? (c) Starting with the initial guesses of 2 and 1 (switching the order in part (a)), find three additional approximations to the root of f ( x ) = x 2 2 using regula falsi. Are these different from the results in (a)? 3. (a) Starting with the initial guesses of 1 and 2, find three additional approximations to the root of f ( x ) = x 2 2 using the secant method. (b) What is the absolute error of the final approximation? You may use the exact (calculator) value of 2 to compute this....
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 Spring '08
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 Approximation

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