This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
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 2Sample Only I. Simpson Rule 1. A calculator is programmed to evaluate (or approximate) a definite integral b a dx x f ) ( using Simpsons 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 cant be found (because its 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 Simpsons rule will yield an...
View Full Document