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Unformatted text preview: Math 4650 Homework #2 Solutions • 1.2 #3ab. Suppose p * must approximate p with relative error at most 10 3 . Find the largest interval in which p * must lie for each value of p . Solution: The relative error is  p * p  p = ε, so that we must have (1 ε ) p ≤ p * ≤ (1 + ε ) p . 999 p ≤ p * ≤ 1 . 001 p. 1. For p = 150 we have 149 . 85 ≤ p * ≤ 150 . 15. 2. For p = 900 we have 899 . 1 ≤ p * ≤ 900 . 9. • 1.2 #5beh. Use threedigit rounding arithmetic to perform the following calculations. Compute the absolute error and relative error with the exact value determined to at least five digits. Solution: b. 133 . 499. The exact answer to five digits is 132 . 50, which rounded to three digits is 133. e. 13 14 6 7 2 e 5 . 4 . The exact answer is 1 . 9535 to five digits. Using rounding arithmetic, we get 13 14 = 0 . 929 and 6 7 = 0 . 857 so that 13 14 6 7 = . 0720. We have e = 2 . 72 so that 2 e = 5 . 44, and 2 e 5 . 4 = 0 . 0400. Hence 13 14 6 7 2 e 5 . 4 = . 0720...
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 Spring '10
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 Math, Exponential Function, Taylor Series, Maclaurin

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