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Math 155 Exam 2-Sample 2006

Math 155 Exam 2-Sample 2006 - 5.4 mi 3.8 4.4 5.5 4.2 4.4...

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Unformatted text preview: 5.4 mi 3.8 4.4 5.5 4.2 4.4 4.7 1.5 0.3 5.4 mi 3.8 4.4 5.5 4.2 4.4 4.7 1.5 0.3 Math 155 Section 02 Calculus II Exam 2—Sample Only I. Simpson’ Rule 1. A calculator is programmed to evaluate (or approximate) a definite integral ∫ b a dx x f ) ( using Simpson’s rule with an error of no more than 1 millionth , with the following instructions: • If K , the least upper bound for | f (4) ( x )| on [ a , b ], is 0, then the calculator will evaluate the integral using 2 sections; • If K can’t be found (because it’s unbounded), then the calculator will evaluate the integral using 1000 sections; and • If K is a real number between 0 and ∞ , then the calculator will evaluate the integral using n sections, where n is the least positive even integer that satisfies the error requirement. a) If the calculator is going to evaluate the following three integrals, determine n , the number of sections needed for each integral (but do not evaluate the integrals, at least not yet). i) ∫ + 3 1 2 4 dx x ii) ∫- 3 1 dx e x iii) ∫- 3 1 3 2 dx x b) For the integral that requires only 2 sections, show that Simpson’s rule will yield an...
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Math 155 Exam 2-Sample 2006 - 5.4 mi 3.8 4.4 5.5 4.2 4.4...

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