# hw1s - 2.2344 2.2422 2.2383 2.2344 2.2383 2.2363 2.2344...

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473/Fall 2009/Homework #1/Solutions (1) a b m 0.0000- 1.0000+ 0.5000- 0.5000- 1.0000+ 0.7500+ 0.5000- 0.7500+ 0.6250 (2) (a) a b m 0.0000- 1.0000+ 0.5000- 0.5000- 1.0000+ 0.7500+ 0.5000- 0.7500+ 0.6250+ 0.5000- 0.6250+ 0.5625- 0.5625- 0.6250+ 0.5938+ 0.5625- 0.5938+ 0.5781- 0.5781- 0.5938+ 0.5859+ (b) a b m 3.2000- 4.0000+ 3.6000+ 3.2000- 3.6000+ 3.4000- 3.4000- 3.6000+ 3.5000+ 3.4000- 3.5000+ 3.4500+ 3.4000- 3.4500+ 3.4250+ 3.4000- 3.4250+ 3.4125- 3.4125- 3.4250+ 3.4188+ (3) a b m 2.0000- 3.0000+ 2.5000+ 2.0000- 2.5000+ 2.2500+ 2.0000- 2.2500+ 2.1250- 2.1250- 2.2500+ 2.1875- 2.1875- 2.2500+ 2.2188- 2.2188- 2.2500+ 2.2344- 2.2344- 2.2500+ 2.2422+

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Unformatted text preview: 2.2344- 2.2422+ 2.2383+ 2.2344- 2.2383+ 2.2363+ 2.2344- 2.2363+ 2.2354-(4) After n iterations, the maximum error is ( b-a ) / 2 n . We have to solve the inequality 3 2 n < 10-6 , giving n > log 2 3 × 10 6 ’ 21 . 5. Since n has to be an integer, we need at least 22 iterations. 1 2 (5) The ﬁrst few iterations are: a b m 1.5000+ 1.6000- 1.5500+ 1.5500+ 1.6000- 1.5750-1.5500+ 1.5750- 1.5625+ 1.5625+ 1.5750- 1.5688+ 1.5688+ 1.5750- 1.5719-1.5688+ 1.5719- 1.5703+ 1.5703+ 1.5719- 1.5711-However, the function has no root in the interval....
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hw1s - 2.2344 2.2422 2.2383 2.2344 2.2383 2.2363 2.2344...

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