ma252f04finalkey - Math 252 Fall 2004 Scarborough Final...

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Math 252, Fall 2004 NAME (print) _________ KEY __________________________ Scarborough Final Exam NAME (sign) ________________________________________ Student Number ______________________________________ This exam is closed book. Notes are not allowed. A Calculator is required. Calculators may only be used to plot graphs and for numerical calculations. The advanced symbolic features of some calculators may not be used on this exam and such answers will not be accepted. For full credit show all work. Part of the grading will be based on proper use of notation. This exam has 9 pages with 11 problems. You should scan all the problems before you begin the test so you can plan out your time. The time limit on this exam is 1 hour 50 minutes. If more room is needed please use the back of the pages. You may find the following formulas of interest: ± x = b ² a n x i = a + i ± x R n = f ( x 0 ) + f ( x 2 ) + f ( x 3 ) + ± + f ( x n ± 1 ) [ ] ² x L n = f ( x 1 ) + f ( x 2 ) + f ( x 3 ) + ± + f ( x n ) [ ] ± x M n = f x 0 + x 1 2 ± ² ³ ´ µ + f x 1 + x 2 2 ± ² ³ ´ µ + f x 2 + x 3 2 ± ² ³ ´ µ + ± + f x n · 1 + x n 2 ± ² ³ ´ µ ¸ ¹ º » ¼ ½ ¾ x T n = 1 2 f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + ± + 2 f ( x n ² 1 ) + f ( x n ) [ ] ± x E M n ± K ( b ² a ) 3 24 n 2 and E T n ± K ( b ² a ) 3 12 n 2 where ³³ f ( x ) ± K for a ± x ± b S n = 1 3 f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + ± + 2 f ( x n ± 2 ) + 4 f ( x n ± 1 ) + f ( x n ) [ ] ² x where n is even E S n ± K ( b ² a ) 5 180 n 4 where f (4) ( x ) ± K for a ± x ± b
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